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    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherExpense_label_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Other Expense</link:label>
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    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherNoncurrentLiabilities_4b301719-b544-40a0-a960-c4f26f895d2d_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherNoncurrentLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Increase (decrease) in other long-term liabilities</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherNoncurrentLiabilities_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherNoncurrentLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Increase (Decrease) in Other Noncurrent Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOtherNoncurrentLiabilities" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_IncreaseDecreaseInOtherNoncurrentLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOtherNoncurrentLiabilities" xlink:to="lab_us-gaap_IncreaseDecreaseInOtherNoncurrentLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredIncomeTaxLiabilitiesNet_4ea8e42d-c6c9-43cc-9496-c6f37104543a_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxLiabilitiesNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Deferred income tax liability</link:label>
    <link:label id="lab_us-gaap_DeferredIncomeTaxLiabilitiesNet_label_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxLiabilitiesNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Deferred Income Tax Liabilities, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredIncomeTaxLiabilitiesNet" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_DeferredIncomeTaxLiabilitiesNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredIncomeTaxLiabilitiesNet" xlink:to="lab_us-gaap_DeferredIncomeTaxLiabilitiesNet" xlink:type="arc" order="1"/>
    <link:label id="lab_ns_InvestmentInSubsidiaries_be0da8ff-5578-40b9-8d7d-5a9fd87d210c_terseLabel_en-US" xlink:label="lab_ns_InvestmentInSubsidiaries" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Investment in subsidiaries</link:label>
    <link:label id="lab_ns_InvestmentInSubsidiaries_label_en-US" xlink:label="lab_ns_InvestmentInSubsidiaries" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Investment in Subsidiaries</link:label>
    <link:label id="lab_ns_InvestmentInSubsidiaries_documentation_en-US" xlink:label="lab_ns_InvestmentInSubsidiaries" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Investments in subsidiaries</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ns_InvestmentInSubsidiaries" xlink:href="ns-20200930.xsd#ns_InvestmentInSubsidiaries"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ns_InvestmentInSubsidiaries" xlink:to="lab_ns_InvestmentInSubsidiaries" xlink:type="arc" order="1"/>
    <link:label id="lab_ns_TexasCityTXOwnershipInterestMember_15b15fe9-4c7b-47c2-a966-5845335a6b59_terseLabel_en-US" xlink:label="lab_ns_TexasCityTXOwnershipInterestMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Texas City, TX Ownership Interest [Member]</link:label>
    <link:label id="lab_ns_TexasCityTXOwnershipInterestMember_label_en-US" xlink:label="lab_ns_TexasCityTXOwnershipInterestMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Texas City, TX Ownership Interest [Member]</link:label>
    <link:label id="lab_ns_TexasCityTXOwnershipInterestMember_documentation_en-US" xlink:label="lab_ns_TexasCityTXOwnershipInterestMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Texas City, TX ownership interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ns_TexasCityTXOwnershipInterestMember" xlink:href="ns-20200930.xsd#ns_TexasCityTXOwnershipInterestMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ns_TexasCityTXOwnershipInterestMember" xlink:to="lab_ns_TexasCityTXOwnershipInterestMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfDebt_d5a2fde7-1318-465a-801d-c465d1f395f7_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other debt borrowings</link:label>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfDebt_label_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Proceeds from Issuance of Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromIssuanceOfDebt" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_ProceedsFromIssuanceOfDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromIssuanceOfDebt" xlink:to="lab_us-gaap_ProceedsFromIssuanceOfDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_SecurityExchangeName_7a2453f1-08a5-41f9-a02f-0c3008695f53_terseLabel_en-US" xlink:label="lab_dei_SecurityExchangeName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Security Exchange Name</link:label>
    <link:label id="lab_dei_SecurityExchangeName_label_en-US" xlink:label="lab_dei_SecurityExchangeName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Security Exchange Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_SecurityExchangeName" xlink:href="https://xbrl.sec.gov/dei/2020/dei-2020-01-31.xsd#dei_SecurityExchangeName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_SecurityExchangeName" xlink:to="lab_dei_SecurityExchangeName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IntangibleAssetsNetExcludingGoodwill_2f8d3437-dc58-41b1-adbe-28772f31137e_terseLabel_en-US" xlink:label="lab_us-gaap_IntangibleAssetsNetExcludingGoodwill" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Intangible assets, net</link:label>
    <link:label id="lab_us-gaap_IntangibleAssetsNetExcludingGoodwill_label_en-US" xlink:label="lab_us-gaap_IntangibleAssetsNetExcludingGoodwill" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Intangible Assets, Net (Excluding Goodwill)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IntangibleAssetsNetExcludingGoodwill" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_IntangibleAssetsNetExcludingGoodwill"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IntangibleAssetsNetExcludingGoodwill" xlink:to="lab_us-gaap_IntangibleAssetsNetExcludingGoodwill" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentUnusedBorrowingCapacityAmount_c898fd11-3cc5-4448-966d-8a8bf235c7ba_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentUnusedBorrowingCapacityAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Debt instrument, unused borrowing capacity, amount</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentUnusedBorrowingCapacityAmount_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentUnusedBorrowingCapacityAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Debt Instrument, Unused Borrowing Capacity, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentUnusedBorrowingCapacityAmount" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_DebtInstrumentUnusedBorrowingCapacityAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentUnusedBorrowingCapacityAmount" xlink:to="lab_us-gaap_DebtInstrumentUnusedBorrowingCapacityAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfLongTermDebt_09bce901-5ff1-4212-aa25-c69d2602dfa5_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfLongTermDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Proceeds from Issuance of Long-term Debt</link:label>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfLongTermDebt_label_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfLongTermDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Proceeds from Issuance of Long-term Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromIssuanceOfLongTermDebt" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_ProceedsFromIssuanceOfLongTermDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromIssuanceOfLongTermDebt" xlink:to="lab_us-gaap_ProceedsFromIssuanceOfLongTermDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ContractWithCustomerAssetNetAbstract_86e031d6-d98f-4de0-b3f6-c966fb1e27c1_terseLabel_en-US" xlink:label="lab_us-gaap_ContractWithCustomerAssetNetAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Contract assets</link:label>
    <link:label id="lab_us-gaap_ContractWithCustomerAssetNetAbstract_label_en-US" xlink:label="lab_us-gaap_ContractWithCustomerAssetNetAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Contract with Customer, Asset, after Allowance for Credit Loss [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractWithCustomerAssetNetAbstract" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_ContractWithCustomerAssetNetAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ContractWithCustomerAssetNetAbstract" xlink:to="lab_us-gaap_ContractWithCustomerAssetNetAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingIncomeLoss_30cb7f68-3004-49d9-bb7c-57c4d93e5042_totalLabel_en-US" xlink:label="lab_us-gaap_OperatingIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Operating income</link:label>
    <link:label id="lab_us-gaap_OperatingIncomeLoss_d1ecdfb1-cecb-4387-9544-5d5c7d46ae77_verboseLabel_en-US" xlink:label="lab_us-gaap_OperatingIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Operating income (loss)</link:label>
    <link:label id="lab_us-gaap_OperatingIncomeLoss_label_en-US" xlink:label="lab_us-gaap_OperatingIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Operating Income (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingIncomeLoss" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_OperatingIncomeLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingIncomeLoss" xlink:to="lab_us-gaap_OperatingIncomeLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CapitalExpenditureDiscontinuedOperations_6c67d677-ee80-4e94-a0f5-4a7dbee2b2d3_negatedLabel_en-US" xlink:label="lab_us-gaap_CapitalExpenditureDiscontinuedOperations" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Capital expenditures</link:label>
    <link:label id="lab_us-gaap_CapitalExpenditureDiscontinuedOperations_label_en-US" xlink:label="lab_us-gaap_CapitalExpenditureDiscontinuedOperations" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Capital Expenditure, Discontinued Operations</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CapitalExpenditureDiscontinuedOperations" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_CapitalExpenditureDiscontinuedOperations"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CapitalExpenditureDiscontinuedOperations" xlink:to="lab_us-gaap_CapitalExpenditureDiscontinuedOperations" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesCurrent_a0be37ea-66d7-498b-b525-0ef9080d86e7_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Total current liabilities</link:label>
    <link:label id="lab_us-gaap_LiabilitiesCurrent_label_en-US" xlink:label="lab_us-gaap_LiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Liabilities, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesCurrent" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_LiabilitiesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesCurrent" xlink:to="lab_us-gaap_LiabilitiesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_ns_PreferredStockDividendAmountPerUnitPerDistributionPeriod_bea7e584-606c-4daa-aa18-04564a84071e_terseLabel_en-US" xlink:label="lab_ns_PreferredStockDividendAmountPerUnitPerDistributionPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred stock, dividend amount, per unit</link:label>
    <link:label id="lab_ns_PreferredStockDividendAmountPerUnitPerDistributionPeriod_label_en-US" xlink:label="lab_ns_PreferredStockDividendAmountPerUnitPerDistributionPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred Stock, Dividend Amount, Per Unit, Per Distribution Period</link:label>
    <link:label id="lab_ns_PreferredStockDividendAmountPerUnitPerDistributionPeriod_documentation_en-US" xlink:label="lab_ns_PreferredStockDividendAmountPerUnitPerDistributionPeriod" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">The dividend amount per unit on preferred stock for the distribution period.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ns_PreferredStockDividendAmountPerUnitPerDistributionPeriod" xlink:href="ns-20200930.xsd#ns_PreferredStockDividendAmountPerUnitPerDistributionPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ns_PreferredStockDividendAmountPerUnitPerDistributionPeriod" xlink:to="lab_ns_PreferredStockDividendAmountPerUnitPerDistributionPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ContractWithCustomerAssetAndLiabilityTableTextBlock_8811db4e-5331-48dc-a811-9e0162b4c0f7_terseLabel_en-US" xlink:label="lab_us-gaap_ContractWithCustomerAssetAndLiabilityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Contract with Customer, Asset and Liability [Table Text Block]</link:label>
    <link:label id="lab_us-gaap_ContractWithCustomerAssetAndLiabilityTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ContractWithCustomerAssetAndLiabilityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Contract with Customer, Contract Asset, Contract Liability, and Receivable [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractWithCustomerAssetAndLiabilityTableTextBlock" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_ContractWithCustomerAssetAndLiabilityTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ContractWithCustomerAssetAndLiabilityTableTextBlock" xlink:to="lab_us-gaap_ContractWithCustomerAssetAndLiabilityTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestrictedCashAndCashEquivalentsItemsLineItems_f99ceb66-ee5b-45fc-8bb0-bf348c290d7d_terseLabel_en-US" xlink:label="lab_us-gaap_RestrictedCashAndCashEquivalentsItemsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Restricted Cash and Cash Equivalents Items [Line Items]</link:label>
    <link:label id="lab_us-gaap_RestrictedCashAndCashEquivalentsItemsLineItems_label_en-US" xlink:label="lab_us-gaap_RestrictedCashAndCashEquivalentsItemsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Restricted Cash and Cash Equivalents Items [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedCashAndCashEquivalentsItemsLineItems" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_RestrictedCashAndCashEquivalentsItemsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestrictedCashAndCashEquivalentsItemsLineItems" xlink:to="lab_us-gaap_RestrictedCashAndCashEquivalentsItemsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_ns_PartnersCapitalOtherIncludingTemporaryEquity_6ee0fee3-6550-4cad-b329-9bc89eb1ee33_terseLabel_en-US" xlink:label="lab_ns_PartnersCapitalOtherIncludingTemporaryEquity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other, including temporary equity</link:label>
    <link:label id="lab_ns_PartnersCapitalOtherIncludingTemporaryEquity_label_en-US" xlink:label="lab_ns_PartnersCapitalOtherIncludingTemporaryEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Partners' Capital, Other, Including Temporary Equity</link:label>
    <link:label id="lab_ns_PartnersCapitalOtherIncludingTemporaryEquity_documentation_en-US" xlink:label="lab_ns_PartnersCapitalOtherIncludingTemporaryEquity" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Partners' capital, other, including temporary equity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ns_PartnersCapitalOtherIncludingTemporaryEquity" xlink:href="ns-20200930.xsd#ns_PartnersCapitalOtherIncludingTemporaryEquity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ns_PartnersCapitalOtherIncludingTemporaryEquity" xlink:to="lab_ns_PartnersCapitalOtherIncludingTemporaryEquity" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_AssetsAbstract_e8623ac8-70e6-4e80-a766-d351b235c5aa_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Assets</link:label>
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    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationInterestIncome_95f3d86a-e511-4fb1-85c5-a799e11f2ba0_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationInterestIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Interest income, net</link:label>
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    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTax_d9bb56a0-653f-4cb2-bb85-55e8f2520bc3_verboseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTax" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other comprehensive income (loss)</link:label>
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    <link:label id="lab_us-gaap_AccountsPayableCurrent_514dbabd-67a8-4727-b15b-aaef02fe8b11_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsPayableCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accounts payable</link:label>
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    <link:label id="lab_us-gaap_SubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipOwnershipInterest_c394f059-0766-4c0f-95d9-e6460cdf5a81_terseLabel_en-US" xlink:label="lab_us-gaap_SubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipOwnershipInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Subsidiary of Limited Liability Company or Limited Partnership, Ownership Interest</link:label>
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    <link:label id="lab_us-gaap_UnusualOrInfrequentItemLineItems_669e4dad-2b25-4380-9742-befa89c444b9_terseLabel_en-US" xlink:label="lab_us-gaap_UnusualOrInfrequentItemLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Unusual or Infrequent Item, or Both [Line Items]</link:label>
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    <link:label id="lab_ns_NustarEnergyLpMember_71449557-b192-4ea3-a6eb-aba383ff540f_terseLabel_en-US" xlink:label="lab_ns_NustarEnergyLpMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">NuStar Energy</link:label>
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    <link:label id="lab_ns_PreferredStockDistributionsPeriodDuringWhichRateIsEffectiveJune292018toJune282020Member_6caa373a-9e4a-4122-a8ef-dbc16b294b8c_terseLabel_en-US" xlink:label="lab_ns_PreferredStockDistributionsPeriodDuringWhichRateIsEffectiveJune292018toJune282020Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred Stock, Distributions, Period - June 29, 2018 to June 28, 2020 [Member]</link:label>
    <link:label id="lab_ns_PreferredStockDistributionsPeriodDuringWhichRateIsEffectiveJune292018toJune282020Member_label_en-US" xlink:label="lab_ns_PreferredStockDistributionsPeriodDuringWhichRateIsEffectiveJune292018toJune282020Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred Stock, Distributions, Period During Which Rate Is Effective - June 29, 2018 to June 28, 2020 [Member]</link:label>
    <link:label id="lab_ns_PreferredStockDistributionsPeriodDuringWhichRateIsEffectiveJune292018toJune282020Member_documentation_en-US" xlink:label="lab_ns_PreferredStockDistributionsPeriodDuringWhichRateIsEffectiveJune292018toJune282020Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred Stock, Distributions, Period - June 29, 2018 to June 28, 2020.</link:label>
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    <link:label id="lab_us-gaap_DebtInstrumentUnamortizedDiscount_b1fee567-1624-48da-8013-2e19928db78a_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentUnamortizedDiscount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Long-term debt, original issue discount</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentUnamortizedDiscount" xlink:to="lab_us-gaap_DebtInstrumentUnamortizedDiscount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GainsLossesOnExtinguishmentOfDebt_d0ade172-85c4-4732-a4cd-d961848e1e4c_terseLabel_en-US" xlink:label="lab_us-gaap_GainsLossesOnExtinguishmentOfDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Loss on extinguishment of debt</link:label>
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    <link:label id="lab_us-gaap_TemporaryEquityOtherChanges_6b02ff0b-6376-41a9-bb7c-14c8058e1460_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityOtherChanges" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other, temporary equity</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquityOtherChanges" xlink:to="lab_us-gaap_TemporaryEquityOtherChanges" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtAndCapitalLeaseObligations_225056f5-3935-4b75-b911-f6ddce8df796_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtAndCapitalLeaseObligations" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Long-term debt, less current portion</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtAndCapitalLeaseObligations" xlink:to="lab_us-gaap_LongTermDebtAndCapitalLeaseObligations" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MajorCustomersAxis_ddad1373-d043-43f8-bae5-b66565783c0b_terseLabel_en-US" xlink:label="lab_srt_MajorCustomersAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Customer [Axis]</link:label>
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    <link:label id="lab_ns_PercentOfAvailableCashDistributed_3da940cc-4a4e-43d0-95fe-56f247fcc373_terseLabel_en-US" xlink:label="lab_ns_PercentOfAvailableCashDistributed" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Percent of available cash distributed</link:label>
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    <link:label id="lab_ns_PercentOfAvailableCashDistributed_documentation_en-US" xlink:label="lab_ns_PercentOfAvailableCashDistributed" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Percent of available cash distributed to partners (per the terms of the partnership agreement).</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ns_PercentOfAvailableCashDistributed" xlink:href="ns-20200930.xsd#ns_PercentOfAvailableCashDistributed"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ns_PercentOfAvailableCashDistributed" xlink:to="lab_ns_PercentOfAvailableCashDistributed" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ContractWithCustomerAssetReclassifiedToReceivable_2dd14bc1-1cd9-4dc2-b1e8-012327b1ddd8_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_ContractWithCustomerAssetReclassifiedToReceivable" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Transfer to accounts receivable</link:label>
    <link:label id="lab_us-gaap_ContractWithCustomerAssetReclassifiedToReceivable_label_en-US" xlink:label="lab_us-gaap_ContractWithCustomerAssetReclassifiedToReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Contract with Customer, Asset, Reclassified to Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractWithCustomerAssetReclassifiedToReceivable" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_ContractWithCustomerAssetReclassifiedToReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ContractWithCustomerAssetReclassifiedToReceivable" xlink:to="lab_us-gaap_ContractWithCustomerAssetReclassifiedToReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnusualOrInfrequentItemInsuranceProceeds_e88f9aaf-64d8-4faa-94ad-a08f12c6d19e_terseLabel_en-US" xlink:label="lab_us-gaap_UnusualOrInfrequentItemInsuranceProceeds" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Insurance proceeds received</link:label>
    <link:label id="lab_us-gaap_UnusualOrInfrequentItemInsuranceProceeds_label_en-US" xlink:label="lab_us-gaap_UnusualOrInfrequentItemInsuranceProceeds" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Unusual or Infrequent Item, or Both, Insurance Proceeds</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnusualOrInfrequentItemInsuranceProceeds" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_UnusualOrInfrequentItemInsuranceProceeds"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnusualOrInfrequentItemInsuranceProceeds" xlink:to="lab_us-gaap_UnusualOrInfrequentItemInsuranceProceeds" xlink:type="arc" order="1"/>
    <link:label id="lab_ns_GoZoneBondsDueDecember2040Member_9961ee18-924d-4ea8-94f5-c34f7ffd987a_terseLabel_en-US" xlink:label="lab_ns_GoZoneBondsDueDecember2040Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">GoZone Bonds Due December 2040</link:label>
    <link:label id="lab_ns_GoZoneBondsDueDecember2040Member_label_en-US" xlink:label="lab_ns_GoZoneBondsDueDecember2040Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">GoZone Bonds Due December 2040 [Member]</link:label>
    <link:label id="lab_ns_GoZoneBondsDueDecember2040Member_documentation_en-US" xlink:label="lab_ns_GoZoneBondsDueDecember2040Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">GoZone Bonds Due December 2040</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ns_GoZoneBondsDueDecember2040Member" xlink:href="ns-20200930.xsd#ns_GoZoneBondsDueDecember2040Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ns_GoZoneBondsDueDecember2040Member" xlink:to="lab_ns_GoZoneBondsDueDecember2040Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HedgingDesignationDomain_7e11e3b9-8c53-470a-9d97-675322736996_terseLabel_en-US" xlink:label="lab_us-gaap_HedgingDesignationDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Hedging Designation [Domain]</link:label>
    <link:label id="lab_us-gaap_HedgingDesignationDomain_label_en-US" xlink:label="lab_us-gaap_HedgingDesignationDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Hedging Designation [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HedgingDesignationDomain" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_HedgingDesignationDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HedgingDesignationDomain" xlink:to="lab_us-gaap_HedgingDesignationDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_ns_DescriptionOfAssetsSold_cee84a23-2d08-4660-99fd-86fd92ffa7c2_terseLabel_en-US" xlink:label="lab_ns_DescriptionOfAssetsSold" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Description of assets sold</link:label>
    <link:label id="lab_ns_DescriptionOfAssetsSold_label_en-US" xlink:label="lab_ns_DescriptionOfAssetsSold" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Description of Assets Sold</link:label>
    <link:label id="lab_ns_DescriptionOfAssetsSold_documentation_en-US" xlink:label="lab_ns_DescriptionOfAssetsSold" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Description of assets sold</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ns_DescriptionOfAssetsSold" xlink:href="ns-20200930.xsd#ns_DescriptionOfAssetsSold"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ns_DescriptionOfAssetsSold" xlink:to="lab_ns_DescriptionOfAssetsSold" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsPerOutstandingLimitedPartnershipUnitBasicNetOfTax_4fcf7108-ea98-435c-9fa3-d9c6b0942197_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsPerOutstandingLimitedPartnershipUnitBasicNetOfTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Continuing operations</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsPerOutstandingLimitedPartnershipUnitBasicNetOfTax_label_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsPerOutstandingLimitedPartnershipUnitBasicNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Income (Loss) from Continuing Operations, Per Outstanding Limited Partnership Unit, Basic, Net of Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromContinuingOperationsPerOutstandingLimitedPartnershipUnitBasicNetOfTax" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_IncomeLossFromContinuingOperationsPerOutstandingLimitedPartnershipUnitBasicNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeLossFromContinuingOperationsPerOutstandingLimitedPartnershipUnitBasicNetOfTax" xlink:to="lab_us-gaap_IncomeLossFromContinuingOperationsPerOutstandingLimitedPartnershipUnitBasicNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherLiabilitiesNoncurrent_6b7073eb-adf7-452d-8dd1-dd0bb2560c33_terseLabel_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other long-term liabilities</link:label>
    <link:label id="lab_us-gaap_OtherLiabilitiesNoncurrent_label_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other Liabilities, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLiabilitiesNoncurrent" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_OtherLiabilitiesNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherLiabilitiesNoncurrent" xlink:to="lab_us-gaap_OtherLiabilitiesNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities_a79e126c-7800-4a84-b574-3e314fa0f14e_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other, net</link:label>
    <link:label id="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities_label_en-US" xlink:label="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Payments for (Proceeds from) Other Investing Activities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_PaymentsForProceedsFromOtherInvestingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:to="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentInformationTable_680c492a-cef8-4cf9-b23b-4b2ea4d1dd52_terseLabel_en-US" xlink:label="lab_dei_DocumentInformationTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Document Information [Table]</link:label>
    <link:label id="lab_dei_DocumentInformationTable_label_en-US" xlink:label="lab_dei_DocumentInformationTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Document Information [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentInformationTable" xlink:href="https://xbrl.sec.gov/dei/2020/dei-2020-01-31.xsd#dei_DocumentInformationTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentInformationTable" xlink:to="lab_dei_DocumentInformationTable" xlink:type="arc" order="1"/>
    <link:label id="lab_ns_ContractWithCustomerAssetTransferToRevenues_74e296cf-58b6-4304-8c58-bad19aed2e03_negatedTerseLabel_en-US" xlink:label="lab_ns_ContractWithCustomerAssetTransferToRevenues" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Transfer to revenues, including amounts reported in discontinued operations, contract assets</link:label>
    <link:label id="lab_ns_ContractWithCustomerAssetTransferToRevenues_label_en-US" xlink:label="lab_ns_ContractWithCustomerAssetTransferToRevenues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Contract with Customer, Asset, Transfer to Revenues</link:label>
    <link:label id="lab_ns_ContractWithCustomerAssetTransferToRevenues_documentation_en-US" xlink:label="lab_ns_ContractWithCustomerAssetTransferToRevenues" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Contract with Customer, Asset, Transfer to Revenues</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ns_ContractWithCustomerAssetTransferToRevenues" xlink:href="ns-20200930.xsd#ns_ContractWithCustomerAssetTransferToRevenues"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ns_ContractWithCustomerAssetTransferToRevenues" xlink:to="lab_ns_ContractWithCustomerAssetTransferToRevenues" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InventoryNet_58ade45c-2f48-4c1a-b74e-511a27b0f317_terseLabel_en-US" xlink:label="lab_us-gaap_InventoryNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Inventories</link:label>
    <link:label id="lab_us-gaap_InventoryNet_label_en-US" xlink:label="lab_us-gaap_InventoryNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Inventory, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InventoryNet" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_InventoryNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InventoryNet" xlink:to="lab_us-gaap_InventoryNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_8af6ab87-c514-461c-b486-7274ce1bffd8_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Revenues from contracts with customers</link:label>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_label_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Revenue from Contract with Customer, Excluding Assessed Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:to="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:type="arc" order="1"/>
    <link:label id="lab_ns_StorageTerminalMember_a6c58e63-0775-4386-b758-26d3242a4282_terseLabel_en-US" xlink:label="lab_ns_StorageTerminalMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Storage Terminal [Member]</link:label>
    <link:label id="lab_ns_StorageTerminalMember_label_en-US" xlink:label="lab_ns_StorageTerminalMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Storage Terminal [Member]</link:label>
    <link:label id="lab_ns_StorageTerminalMember_documentation_en-US" xlink:label="lab_ns_StorageTerminalMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Storage Terminal</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ns_StorageTerminalMember" xlink:href="ns-20200930.xsd#ns_StorageTerminalMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ns_StorageTerminalMember" xlink:to="lab_ns_StorageTerminalMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ns_SeriesAPreferredLimitedPartnerMember_95e03539-9351-47d0-9b79-051da2e1fd8c_terseLabel_en-US" xlink:label="lab_ns_SeriesAPreferredLimitedPartnerMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Series A Preferred Limited Partner [Member]</link:label>
    <link:label id="lab_ns_SeriesAPreferredLimitedPartnerMember_label_en-US" xlink:label="lab_ns_SeriesAPreferredLimitedPartnerMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Series A Preferred Limited Partner [Member]</link:label>
    <link:label id="lab_ns_SeriesAPreferredLimitedPartnerMember_documentation_en-US" xlink:label="lab_ns_SeriesAPreferredLimitedPartnerMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Series A Preferred Limited Partner - Partner with preferential rights over the common limited partner in areas that could include, but are not limited to, liquidation, redemption, conversion, tax status of distribution or sharing in distributions.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ns_SeriesAPreferredLimitedPartnerMember" xlink:href="ns-20200930.xsd#ns_SeriesAPreferredLimitedPartnerMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ns_SeriesAPreferredLimitedPartnerMember" xlink:to="lab_ns_SeriesAPreferredLimitedPartnerMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementLineItems_b3c5181c-709b-497d-8638-c0d1d12e693a_terseLabel_en-US" xlink:label="lab_us-gaap_StatementLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Statement [Line Items]</link:label>
    <link:label id="lab_us-gaap_StatementLineItems_label_en-US" xlink:label="lab_us-gaap_StatementLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Statement [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementLineItems" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_StatementLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementLineItems" xlink:to="lab_us-gaap_StatementLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PartnersCapitalAbstract_ad1fb6ab-6c52-42f8-b0be-221b18ac1fee_terseLabel_en-US" xlink:label="lab_us-gaap_PartnersCapitalAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Partners&#8217; equity (Note 9):</link:label>
    <link:label id="lab_us-gaap_PartnersCapitalAbstract_label_en-US" xlink:label="lab_us-gaap_PartnersCapitalAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Partners' Capital [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PartnersCapitalAbstract" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_PartnersCapitalAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PartnersCapitalAbstract" xlink:to="lab_us-gaap_PartnersCapitalAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ScenarioForecastMember_dcf4d722-0c9a-47f4-93d0-76ec56b94c10_terseLabel_en-US" xlink:label="lab_srt_ScenarioForecastMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Forecast [Member]</link:label>
    <link:label id="lab_srt_ScenarioForecastMember_label_en-US" xlink:label="lab_srt_ScenarioForecastMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Forecast [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ScenarioForecastMember" xlink:href="http://xbrl.fasb.org/srt/2020/elts/srt-2020-01-31.xsd#srt_ScenarioForecastMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ScenarioForecastMember" xlink:to="lab_srt_ScenarioForecastMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfStockDomain_bcf6035b-835d-43d7-a7eb-9ef0f48c4523_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfStockDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Class of Stock [Domain]</link:label>
    <link:label id="lab_us-gaap_ClassOfStockDomain_label_en-US" xlink:label="lab_us-gaap_ClassOfStockDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Class of Stock [Domain]</link:label>
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    <link:label id="lab_us-gaap_ProceedsFromLongTermLinesOfCredit_73990c00-babc-4669-907d-4a463ee348db_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromLongTermLinesOfCredit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Proceeds from other long-term debt borrowings</link:label>
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    <link:label id="lab_us-gaap_InterestPayableCurrent_3faa39b0-158a-480e-8400-6ad10c5d28c1_terseLabel_en-US" xlink:label="lab_us-gaap_InterestPayableCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accrued interest payable</link:label>
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    <link:label id="lab_us-gaap_StatementTable_36fdc37e-ab67-439a-b81b-50f0f1c904a2_terseLabel_en-US" xlink:label="lab_us-gaap_StatementTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Statement [Table]</link:label>
    <link:label id="lab_us-gaap_StatementTable_label_en-US" xlink:label="lab_us-gaap_StatementTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Statement [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementTable" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_StatementTable"/>
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    <link:label id="lab_us-gaap_OtherComprehensiveIncomeOtherNetOfTax_fc9b1700-b6df-46b0-bafc-a7e6a7db59d9_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeOtherNetOfTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeOtherNetOfTax" xlink:to="lab_us-gaap_OtherComprehensiveIncomeOtherNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_ns_PreferredStockDistributionsPeriodDuringWhichRateIsEffectiveAxis_3c102ae9-63ea-47bf-9c1c-54c9209fd4eb_terseLabel_en-US" xlink:label="lab_ns_PreferredStockDistributionsPeriodDuringWhichRateIsEffectiveAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred Stock, Distributions, Period [Axis]</link:label>
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    <link:label id="lab_ns_PreferredStockDistributionsPeriodDuringWhichRateIsEffectiveAxis_documentation_en-US" xlink:label="lab_ns_PreferredStockDistributionsPeriodDuringWhichRateIsEffectiveAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Information about timing of distributions.</link:label>
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    <link:label id="lab_us-gaap_DebtInstrumentFairValue_854b73bf-f307-4625-b5f1-f032c9b39726_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fair value, long-term debt</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentFairValue_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Debt Instrument, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentFairValue" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_DebtInstrumentFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentFairValue" xlink:to="lab_us-gaap_DebtInstrumentFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnusualOrInfrequentItemNatureOfEventOrTransaction_9f74be8b-ca7c-4999-907b-b4af22de084d_terseLabel_en-US" xlink:label="lab_us-gaap_UnusualOrInfrequentItemNatureOfEventOrTransaction" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Impact of fire at Selby, CA terminal</link:label>
    <link:label id="lab_us-gaap_UnusualOrInfrequentItemNatureOfEventOrTransaction_label_en-US" xlink:label="lab_us-gaap_UnusualOrInfrequentItemNatureOfEventOrTransaction" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Unusual or Infrequent Item, or Both, Nature of Event or Transaction</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnusualOrInfrequentItemNatureOfEventOrTransaction" xlink:to="lab_us-gaap_UnusualOrInfrequentItemNatureOfEventOrTransaction" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntitySmallBusiness_676e1304-85be-4e60-a07e-83c8a9543937_terseLabel_en-US" xlink:label="lab_dei_EntitySmallBusiness" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Small Business</link:label>
    <link:label id="lab_dei_EntitySmallBusiness_label_en-US" xlink:label="lab_dei_EntitySmallBusiness" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Small Business</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntitySmallBusiness" xlink:href="https://xbrl.sec.gov/dei/2020/dei-2020-01-31.xsd#dei_EntitySmallBusiness"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntitySmallBusiness" xlink:to="lab_dei_EntitySmallBusiness" xlink:type="arc" order="1"/>
    <link:label id="lab_ns_LogisticsRevolvingCreditAgreementMember_bd8773bc-8ec6-407e-8231-25446bda066c_terseLabel_en-US" xlink:label="lab_ns_LogisticsRevolvingCreditAgreementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Revolving Credit Agreement [Member]</link:label>
    <link:label id="lab_ns_LogisticsRevolvingCreditAgreementMember_label_en-US" xlink:label="lab_ns_LogisticsRevolvingCreditAgreementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Logistics' Revolving Credit Agreement [Member]</link:label>
    <link:label id="lab_ns_LogisticsRevolvingCreditAgreementMember_documentation_en-US" xlink:label="lab_ns_LogisticsRevolvingCreditAgreementMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Logistics' revolving credit agreement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ns_LogisticsRevolvingCreditAgreementMember" xlink:href="ns-20200930.xsd#ns_LogisticsRevolvingCreditAgreementMember"/>
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    <link:label id="lab_us-gaap_NetIncomeLossPerOutstandingLimitedPartnershipUnitBasicNetOfTax_0b1bb6d2-9db4-40bc-853a-554f352bdc4d_totalLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossPerOutstandingLimitedPartnershipUnitBasicNetOfTax" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Total (Note 10)</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossPerOutstandingLimitedPartnershipUnitBasicNetOfTax_d9a1418e-5e70-4a87-b543-93c2d8d9330e_terseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossPerOutstandingLimitedPartnershipUnitBasicNetOfTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Basic net income (loss) per common unit</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossPerOutstandingLimitedPartnershipUnitBasicNetOfTax_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossPerOutstandingLimitedPartnershipUnitBasicNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net Income (Loss), Per Outstanding Limited Partnership Unit, Basic, Net of Tax</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLossPerOutstandingLimitedPartnershipUnitBasicNetOfTax" xlink:to="lab_us-gaap_NetIncomeLossPerOutstandingLimitedPartnershipUnitBasicNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_f8d500bd-ef61-4c9f-b5fa-f0dbe25f4e73_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fair Value Hierarchy and NAV [Domain]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_FairValueMeasurementsFairValueHierarchyDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:to="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtDisclosureTextBlock_08e11547-2b69-4be0-80f8-e33a220570b3_terseLabel_en-US" xlink:label="lab_us-gaap_DebtDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">DEBT</link:label>
    <link:label id="lab_us-gaap_DebtDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_DebtDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Debt Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtDisclosureTextBlock" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_DebtDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtDisclosureTextBlock" xlink:to="lab_us-gaap_DebtDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationRevenue_09624c73-5ec6-4c3a-9193-b6fa4ef416ba_verboseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationRevenue" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Revenues</link:label>
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    <link:label id="lab_us-gaap_BusinessInterruptionLossDomain_e90fe90a-6318-4288-9017-3452fc30cccf_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessInterruptionLossDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Business Interruption Loss [Domain]</link:label>
    <link:label id="lab_us-gaap_BusinessInterruptionLossDomain_label_en-US" xlink:label="lab_us-gaap_BusinessInterruptionLossDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Business Interruption Loss [Domain]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessInterruptionLossDomain" xlink:to="lab_us-gaap_BusinessInterruptionLossDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfRestrictedCashAndCashEquivalentsTable_3c394d02-dc77-4788-9d73-06b612bd1ee9_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfRestrictedCashAndCashEquivalentsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Restrictions on Cash and Cash Equivalents [Table]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfRestrictedCashAndCashEquivalentsTable" xlink:to="lab_us-gaap_ScheduleOfRestrictedCashAndCashEquivalentsTable" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_AmendmentFlag_214d8fe0-27b3-4e69-96d3-a8a0de285825_terseLabel_en-US" xlink:label="lab_dei_AmendmentFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Amendment Flag</link:label>
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    <link:label id="lab_us-gaap_RepaymentsOfDebt_ceee6190-efa2-43a9-b354-5913c860d5bf_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_RepaymentsOfDebt" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Debt repayments</link:label>
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    <link:label id="lab_dei_EntityCentralIndexKey_ad3cb9e9-25bc-48de-9f03-ed0476f840af_terseLabel_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Central Index Key</link:label>
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    <link:label id="lab_ns_ContractwithCustomerLiabilityAdditions_label_en-US" xlink:label="lab_ns_ContractwithCustomerLiabilityAdditions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Contract with Customer, Liability, Additions</link:label>
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    <link:label id="lab_us-gaap_DerivativeInstrumentRiskAxis_50f95fdc-b8d4-4edc-92c2-dcae1354af45_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative Instrument [Axis]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentRiskAxis" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_DerivativeInstrumentRiskAxis"/>
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    <link:label id="lab_ns_AssetsHeldforSaleMember_80eac993-f50c-4ee4-a20d-a0f2d3ebde83_terseLabel_en-US" xlink:label="lab_ns_AssetsHeldforSaleMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Assets held for sale</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventsTextBlock" xlink:to="lab_us-gaap_SubsequentEventsTextBlock" xlink:type="arc" order="1"/>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentPaymentTerms" xlink:to="lab_us-gaap_DebtInstrumentPaymentTerms" xlink:type="arc" order="1"/>
    <link:label id="lab_ns_DistributionPaymentDate_a39bb98e-9fe7-4353-a45d-a62761bbc7b1_verboseLabel_en-US" xlink:label="lab_ns_DistributionPaymentDate" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Distribution payment date</link:label>
    <link:label id="lab_ns_DistributionPaymentDate_label_en-US" xlink:label="lab_ns_DistributionPaymentDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Distribution payment date</link:label>
    <link:label id="lab_ns_DistributionPaymentDate_documentation_en-US" xlink:label="lab_ns_DistributionPaymentDate" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Distribution payment date for distribution earned during the reporting period. Includes distributions to be paid to the limited partners.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ns_DistributionPaymentDate" xlink:href="ns-20200930.xsd#ns_DistributionPaymentDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ns_DistributionPaymentDate" xlink:to="lab_ns_DistributionPaymentDate" xlink:type="arc" order="1"/>
    <link:label id="lab_ns_ParentCompanyGuarantorMember_53a73a9e-6c93-47b7-9f84-a4847c29cceb_terseLabel_en-US" xlink:label="lab_ns_ParentCompanyGuarantorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Parent Company Guarantor [Member]</link:label>
    <link:label id="lab_ns_ParentCompanyGuarantorMember_label_en-US" xlink:label="lab_ns_ParentCompanyGuarantorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Parent Company Guarantor [Member]</link:label>
    <link:label id="lab_ns_ParentCompanyGuarantorMember_documentation_en-US" xlink:label="lab_ns_ParentCompanyGuarantorMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">The registrant that controls, directly or indirectly, another entity (or entities) and has guaranteed the issue of securities by one of its subsidiaries.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ns_ParentCompanyGuarantorMember" xlink:href="ns-20200930.xsd#ns_ParentCompanyGuarantorMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ns_ParentCompanyGuarantorMember" xlink:to="lab_ns_ParentCompanyGuarantorMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipLineItems_a8d02760-25cc-42ef-aff6-17634718d2ec_terseLabel_en-US" xlink:label="lab_us-gaap_SubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Subsidiary of Limited Liability Company or Limited Partnership [Line Items]</link:label>
    <link:label id="lab_us-gaap_SubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipLineItems_label_en-US" xlink:label="lab_us-gaap_SubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Subsidiary of Limited Liability Company or Limited Partnership [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipLineItems" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_SubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipLineItems" xlink:to="lab_us-gaap_SubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentDomain_92e54a6c-6e98-474b-ba96-4ab1820aa729_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Reporting Segment [Domain]</link:label>
    <link:label id="lab_us-gaap_SegmentDomain_5606f957-adf5-4649-bf3c-24f0862d175b_verboseLabel_en-US" xlink:label="lab_us-gaap_SegmentDomain" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Segments [Domain]</link:label>
    <link:label id="lab_us-gaap_SegmentDomain_label_en-US" xlink:label="lab_us-gaap_SegmentDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Segments [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentDomain" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_SegmentDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentDomain" xlink:to="lab_us-gaap_SegmentDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_ns_BusinessInterruptionLossfromSelbyCaliforniaFireMember_9661feda-71b2-4573-a6e6-a8e4a20d2c35_terseLabel_en-US" xlink:label="lab_ns_BusinessInterruptionLossfromSelbyCaliforniaFireMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Business Interruption Loss from Selby, California Fire [Member]</link:label>
    <link:label id="lab_ns_BusinessInterruptionLossfromSelbyCaliforniaFireMember_label_en-US" xlink:label="lab_ns_BusinessInterruptionLossfromSelbyCaliforniaFireMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Business Interruption Loss from Selby, California Fire [Member]</link:label>
    <link:label id="lab_ns_BusinessInterruptionLossfromSelbyCaliforniaFireMember_documentation_en-US" xlink:label="lab_ns_BusinessInterruptionLossfromSelbyCaliforniaFireMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Business Interruption Loss from Selby, California Fire [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ns_BusinessInterruptionLossfromSelbyCaliforniaFireMember" xlink:href="ns-20200930.xsd#ns_BusinessInterruptionLossfromSelbyCaliforniaFireMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ns_BusinessInterruptionLossfromSelbyCaliforniaFireMember" xlink:to="lab_ns_BusinessInterruptionLossfromSelbyCaliforniaFireMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ns_PreferredStockAccretionofRedemptionDiscountIncludingTemporaryEquity_d7390e09-a74c-4299-a13e-0abec1e3be4e_negatedTerseLabel_en-US" xlink:label="lab_ns_PreferredStockAccretionofRedemptionDiscountIncludingTemporaryEquity" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Series D Preferred Unit accretion, total</link:label>
    <link:label id="lab_ns_PreferredStockAccretionofRedemptionDiscountIncludingTemporaryEquity_label_en-US" xlink:label="lab_ns_PreferredStockAccretionofRedemptionDiscountIncludingTemporaryEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred Stock, Accretion of Redemption Discount, Including Temporary Equity</link:label>
    <link:label id="lab_ns_PreferredStockAccretionofRedemptionDiscountIncludingTemporaryEquity_documentation_en-US" xlink:label="lab_ns_PreferredStockAccretionofRedemptionDiscountIncludingTemporaryEquity" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred Stock, Accretion of Redemption Discount, Including Temporary Equity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ns_PreferredStockAccretionofRedemptionDiscountIncludingTemporaryEquity" xlink:href="ns-20200930.xsd#ns_PreferredStockAccretionofRedemptionDiscountIncludingTemporaryEquity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ns_PreferredStockAccretionofRedemptionDiscountIncludingTemporaryEquity" xlink:to="lab_ns_PreferredStockAccretionofRedemptionDiscountIncludingTemporaryEquity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfCashFlowsAbstract_d6c7e2b9-6ac5-4880-9fe9-4184c8145be3_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Statement of Cash Flows [Abstract]</link:label>
    <link:label id="lab_us-gaap_StatementOfCashFlowsAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Statement of Cash Flows [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfCashFlowsAbstract" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_StatementOfCashFlowsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfCashFlowsAbstract" xlink:to="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeLossAttributableToParent_d792bb52-8c26-4ecd-a0ee-0a5777e84bb2_totalLabel_en-US" xlink:label="lab_us-gaap_IncomeLossAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Income (loss) before income tax expense (benefit)</link:label>
    <link:label id="lab_us-gaap_IncomeLossAttributableToParent_label_en-US" xlink:label="lab_us-gaap_IncomeLossAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Income (Loss) Attributable to Parent, before Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossAttributableToParent" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_IncomeLossAttributableToParent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeLossAttributableToParent" xlink:to="lab_us-gaap_IncomeLossAttributableToParent" xlink:type="arc" order="1"/>
    <link:label id="lab_ns_ThroughputTerminalMember_a2b5ccca-47df-41c8-9a2d-b28d6dfeaccc_terseLabel_en-US" xlink:label="lab_ns_ThroughputTerminalMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Throughput Terminal [Member]</link:label>
    <link:label id="lab_ns_ThroughputTerminalMember_label_en-US" xlink:label="lab_ns_ThroughputTerminalMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Throughput Terminal [Member]</link:label>
    <link:label id="lab_ns_ThroughputTerminalMember_documentation_en-US" xlink:label="lab_ns_ThroughputTerminalMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Throughput Terminal</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ns_ThroughputTerminalMember" xlink:href="ns-20200930.xsd#ns_ThroughputTerminalMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ns_ThroughputTerminalMember" xlink:to="lab_ns_ThroughputTerminalMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectOfExchangeRateOnCashAndCashEquivalents_6a2aa5c5-3f53-467c-ae5c-e5c6c1034e67_terseLabel_en-US" xlink:label="lab_us-gaap_EffectOfExchangeRateOnCashAndCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Effect of foreign exchange rate changes on cash</link:label>
    <link:label id="lab_us-gaap_EffectOfExchangeRateOnCashAndCashEquivalents_label_en-US" xlink:label="lab_us-gaap_EffectOfExchangeRateOnCashAndCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Effect of Exchange Rate on Cash and Cash Equivalents</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectOfExchangeRateOnCashAndCashEquivalents" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_EffectOfExchangeRateOnCashAndCashEquivalents"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EffectOfExchangeRateOnCashAndCashEquivalents" xlink:to="lab_us-gaap_EffectOfExchangeRateOnCashAndCashEquivalents" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeStatementLocationAxis_10dc41d1-30ef-46ee-a76e-625ebee50d0d_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeStatementLocationAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Income Statement Location [Axis]</link:label>
    <link:label id="lab_us-gaap_IncomeStatementLocationAxis_label_en-US" xlink:label="lab_us-gaap_IncomeStatementLocationAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Income Statement Location [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementLocationAxis" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_IncomeStatementLocationAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeStatementLocationAxis" xlink:to="lab_us-gaap_IncomeStatementLocationAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCommonStockSharesOutstanding_9befe8a8-d80f-49f5-927e-6b681df6a310_terseLabel_en-US" xlink:label="lab_dei_EntityCommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Partnership Units Outstanding</link:label>
    <link:label id="lab_dei_EntityCommonStockSharesOutstanding_label_en-US" xlink:label="lab_dei_EntityCommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Common Stock, Shares Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCommonStockSharesOutstanding" xlink:href="https://xbrl.sec.gov/dei/2020/dei-2020-01-31.xsd#dei_EntityCommonStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCommonStockSharesOutstanding" xlink:to="lab_dei_EntityCommonStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeStatementLocationDomain_8b25ee60-7dea-40b5-bac1-970f45229e81_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeStatementLocationDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Income Statement Location [Domain]</link:label>
    <link:label id="lab_us-gaap_IncomeStatementLocationDomain_label_en-US" xlink:label="lab_us-gaap_IncomeStatementLocationDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Income Statement Location [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementLocationDomain" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_IncomeStatementLocationDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeStatementLocationDomain" xlink:to="lab_us-gaap_IncomeStatementLocationDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_ns_SelbyCaliforniaFireMember_d10d2449-015b-4bf6-b5c4-f7b9e9c171b1_terseLabel_en-US" xlink:label="lab_ns_SelbyCaliforniaFireMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Selby, California Fire [Member]</link:label>
    <link:label id="lab_ns_SelbyCaliforniaFireMember_label_en-US" xlink:label="lab_ns_SelbyCaliforniaFireMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Selby, California Fire [Member]</link:label>
    <link:label id="lab_ns_SelbyCaliforniaFireMember_documentation_en-US" xlink:label="lab_ns_SelbyCaliforniaFireMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Selby, California Fire [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ns_SelbyCaliforniaFireMember" xlink:href="ns-20200930.xsd#ns_SelbyCaliforniaFireMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ns_SelbyCaliforniaFireMember" xlink:to="lab_ns_SelbyCaliforniaFireMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_6b3d94a8-4d3d-4bb4-b830-837b7f36ef1b_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Cash flows from financing activities:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net Cash Provided by (Used in) Financing Activities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestRateCashFlowHedgeGainLossToBeReclassifiedDuringNext12MonthsNet_6cd900d8-4070-491a-b6eb-dd5a74f11b81_terseLabel_en-US" xlink:label="lab_us-gaap_InterestRateCashFlowHedgeGainLossToBeReclassifiedDuringNext12MonthsNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Loss to be reclassified during next 12 months</link:label>
    <link:label id="lab_us-gaap_InterestRateCashFlowHedgeGainLossToBeReclassifiedDuringNext12MonthsNet_label_en-US" xlink:label="lab_us-gaap_InterestRateCashFlowHedgeGainLossToBeReclassifiedDuringNext12MonthsNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Interest Rate Cash Flow Hedge Gain (Loss) to be Reclassified During Next 12 Months, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestRateCashFlowHedgeGainLossToBeReclassifiedDuringNext12MonthsNet" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_InterestRateCashFlowHedgeGainLossToBeReclassifiedDuringNext12MonthsNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestRateCashFlowHedgeGainLossToBeReclassifiedDuringNext12MonthsNet" xlink:to="lab_us-gaap_InterestRateCashFlowHedgeGainLossToBeReclassifiedDuringNext12MonthsNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeNotionalAmount_0dc0ea0b-809b-4548-97ff-907efe1d569b_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeNotionalAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Notional amount of forward-starting interest rate swaps</link:label>
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    <link:label id="lab_dei_Security12bTitle_e1e62f49-fc27-4d97-ab8c-11eeec209f62_terseLabel_en-US" xlink:label="lab_dei_Security12bTitle" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Title of 12(b) Security</link:label>
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    <link:label id="lab_us-gaap_DistributionMadeToLimitedPartnerDistributionsPaidPerUnit_02e07b71-4d97-4795-a694-b1c1b851aeda_terseLabel_en-US" xlink:label="lab_us-gaap_DistributionMadeToLimitedPartnerDistributionsPaidPerUnit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Cash distributions paid, per unit</link:label>
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    <link:label id="lab_us-gaap_DiscontinuedOperationIncomeLossFromDiscontinuedOperationBeforeIncomeTax_795f5a3d-fed4-4215-a349-39482bc4ed81_totalLabel_en-US" xlink:label="lab_us-gaap_DiscontinuedOperationIncomeLossFromDiscontinuedOperationBeforeIncomeTax" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">(Loss) income from discontinued operations before income tax expense</link:label>
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    <link:label id="lab_us-gaap_ReportingUnitDomain_12af1d89-00b8-4303-a2e7-a43dfee77bf8_terseLabel_en-US" xlink:label="lab_us-gaap_ReportingUnitDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Reporting Unit [Domain]</link:label>
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    <link:label id="lab_us-gaap_SubsequentEventTypeAxis_d3966fb3-5639-4d26-afb1-ab3d27160b66_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Subsequent Event Type [Axis]</link:label>
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    <link:label id="lab_us-gaap_ContractWithCustomerLiabilityAbstract_e11dc210-d565-48ac-a5d9-083b7ff51fad_terseLabel_en-US" xlink:label="lab_us-gaap_ContractWithCustomerLiabilityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Contract liabilities</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquityAccretionToRedemptionValue" xlink:to="lab_us-gaap_TemporaryEquityAccretionToRedemptionValue" xlink:type="arc" order="1"/>
    <link:label id="lab_ns_InvestmentInWhollyOwnedSubsidiaries_f15c04c2-20de-45a7-91cf-f67832cf09d0_terseLabel_en-US" xlink:label="lab_ns_InvestmentInWhollyOwnedSubsidiaries" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Investment in wholly owned subsidiaries</link:label>
    <link:label id="lab_ns_InvestmentInWhollyOwnedSubsidiaries_label_en-US" xlink:label="lab_ns_InvestmentInWhollyOwnedSubsidiaries" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Investment in Wholly Owned Subsidiaries</link:label>
    <link:label id="lab_ns_InvestmentInWhollyOwnedSubsidiaries_documentation_en-US" xlink:label="lab_ns_InvestmentInWhollyOwnedSubsidiaries" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Investment in Wholly Owned Subsidiaries</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ns_InvestmentInWhollyOwnedSubsidiaries" xlink:href="ns-20200930.xsd#ns_InvestmentInWhollyOwnedSubsidiaries"/>
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    <link:label id="lab_ns_ChangeinContractwithCustomerLiabilityTotal_bf0b0185-0b17-4970-8950-fdace77114a7_negatedLabel_en-US" xlink:label="lab_ns_ChangeinContractwithCustomerLiabilityTotal" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Total activity</link:label>
    <link:label id="lab_ns_ChangeinContractwithCustomerLiabilityTotal_label_en-US" xlink:label="lab_ns_ChangeinContractwithCustomerLiabilityTotal" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Change in Contract with Customer, Liability, Total</link:label>
    <link:label id="lab_ns_ChangeinContractwithCustomerLiabilityTotal_documentation_en-US" xlink:label="lab_ns_ChangeinContractwithCustomerLiabilityTotal" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Total change in contract with customer liability balance in the current period.</link:label>
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    <link:label id="lab_us-gaap_DirectOperatingCosts_d73176d0-5194-4e66-a27c-c237c8fe2fbb_terseLabel_en-US" xlink:label="lab_us-gaap_DirectOperatingCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Operating expenses (excluding depreciation and amortization expense)</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DirectOperatingCosts" xlink:to="lab_us-gaap_DirectOperatingCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DistributionMadeToLimitedPartnerLineItems_7df4d939-6b54-4c11-b8c4-457c428373df_terseLabel_en-US" xlink:label="lab_us-gaap_DistributionMadeToLimitedPartnerLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Distribution Made to Preferred Limited Partner [Line Items]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DistributionMadeToLimitedPartnerLineItems" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_DistributionMadeToLimitedPartnerLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DistributionMadeToLimitedPartnerLineItems" xlink:to="lab_us-gaap_DistributionMadeToLimitedPartnerLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLossPerOutstandingLimitedPartnershipUnitDilutedAbstract_5930e7ac-02f7-41c9-a7cf-d4bf8b759530_terseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossPerOutstandingLimitedPartnershipUnitDilutedAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Diluted net income (loss) per common unit</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossPerOutstandingLimitedPartnershipUnitDilutedAbstract_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossPerOutstandingLimitedPartnershipUnitDilutedAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net Income (Loss), Net of Tax, Per Outstanding Limited Partnership Unit, Diluted [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossPerOutstandingLimitedPartnershipUnitDilutedAbstract" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_NetIncomeLossPerOutstandingLimitedPartnershipUnitDilutedAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLossPerOutstandingLimitedPartnershipUnitDilutedAbstract" xlink:to="lab_us-gaap_NetIncomeLossPerOutstandingLimitedPartnershipUnitDilutedAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ns_DebtExtinguishmentCostsTypeDomain_d059d155-40f4-4a84-a067-75d6e0744af8_terseLabel_en-US" xlink:label="lab_ns_DebtExtinguishmentCostsTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Debt Extinguishment Costs, Type [Domain]</link:label>
    <link:label id="lab_ns_DebtExtinguishmentCostsTypeDomain_label_en-US" xlink:label="lab_ns_DebtExtinguishmentCostsTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Debt Extinguishment Costs, Type [Domain]</link:label>
    <link:label id="lab_ns_DebtExtinguishmentCostsTypeDomain_documentation_en-US" xlink:label="lab_ns_DebtExtinguishmentCostsTypeDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Debt extinguishment costs, type</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ns_DebtExtinguishmentCostsTypeDomain" xlink:href="ns-20200930.xsd#ns_DebtExtinguishmentCostsTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ns_DebtExtinguishmentCostsTypeDomain" xlink:to="lab_ns_DebtExtinguishmentCostsTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_ns_PreferredStockDistributionsPeriodDuringWhichRateIsEffectiveJune292020toJune282023Member_a8b6c92b-fefb-426e-8da3-e2fcde5b7254_terseLabel_en-US" xlink:label="lab_ns_PreferredStockDistributionsPeriodDuringWhichRateIsEffectiveJune292020toJune282023Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred Stock, Distributions, Period - June 29, 2020 to June 28, 2023 [Member]</link:label>
    <link:label id="lab_ns_PreferredStockDistributionsPeriodDuringWhichRateIsEffectiveJune292020toJune282023Member_label_en-US" xlink:label="lab_ns_PreferredStockDistributionsPeriodDuringWhichRateIsEffectiveJune292020toJune282023Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred Stock, Distributions, Period During Which Rate Is Effective - June 29, 2020 to June 28, 2023 [Member]</link:label>
    <link:label id="lab_ns_PreferredStockDistributionsPeriodDuringWhichRateIsEffectiveJune292020toJune282023Member_documentation_en-US" xlink:label="lab_ns_PreferredStockDistributionsPeriodDuringWhichRateIsEffectiveJune292020toJune282023Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred Stock, Distributions, Period - June 29, 2020 to June 28, 2023 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ns_PreferredStockDistributionsPeriodDuringWhichRateIsEffectiveJune292020toJune282023Member" xlink:href="ns-20200930.xsd#ns_PreferredStockDistributionsPeriodDuringWhichRateIsEffectiveJune292020toJune282023Member"/>
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    <link:label id="lab_us-gaap_ProceedsFromSaleOfProductiveAssets_ba18197a-201d-4b00-9139-a1149144c72e_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfProductiveAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Proceeds from sale or disposition of assets</link:label>
    <link:label id="lab_us-gaap_ProceedsFromSaleOfProductiveAssets_label_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfProductiveAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Proceeds from Sale of Productive Assets</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromSaleOfProductiveAssets" xlink:to="lab_us-gaap_ProceedsFromSaleOfProductiveAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ProductOrServiceAxis_9d85b590-7136-4abd-8f35-0b5a271f0ad5_terseLabel_en-US" xlink:label="lab_srt_ProductOrServiceAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Product and Service [Axis]</link:label>
    <link:label id="lab_srt_ProductOrServiceAxis_label_en-US" xlink:label="lab_srt_ProductOrServiceAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Product and Service [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ProductOrServiceAxis" xlink:href="http://xbrl.fasb.org/srt/2020/elts/srt-2020-01-31.xsd#srt_ProductOrServiceAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ProductOrServiceAxis" xlink:to="lab_srt_ProductOrServiceAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Liabilities_77d75d20-c692-44a4-9d97-73fe6d8050ba_totalLabel_en-US" xlink:label="lab_us-gaap_Liabilities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Total liabilities</link:label>
    <link:label id="lab_us-gaap_Liabilities_label_en-US" xlink:label="lab_us-gaap_Liabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Liabilities" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_Liabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Liabilities" xlink:to="lab_us-gaap_Liabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PartnerCapitalComponentsAxis_21e0c19a-e2ee-4bb1-a9e7-de1efce42643_terseLabel_en-US" xlink:label="lab_us-gaap_PartnerCapitalComponentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Partner Capital Components [Axis]</link:label>
    <link:label id="lab_us-gaap_PartnerCapitalComponentsAxis_label_en-US" xlink:label="lab_us-gaap_PartnerCapitalComponentsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Partner Capital Components [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PartnerCapitalComponentsAxis" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_PartnerCapitalComponentsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PartnerCapitalComponentsAxis" xlink:to="lab_us-gaap_PartnerCapitalComponentsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfUnsecuredDebt_ef161110-504c-42c0-b4c0-e73d825d1403_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfUnsecuredDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Proceeds from Term Loan, net of discount and issuance costs</link:label>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfUnsecuredDebt_label_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfUnsecuredDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Proceeds from Issuance of Unsecured Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromIssuanceOfUnsecuredDebt" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_ProceedsFromIssuanceOfUnsecuredDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromIssuanceOfUnsecuredDebt" xlink:to="lab_us-gaap_ProceedsFromIssuanceOfUnsecuredDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherNoncurrentAssetsMember_9d75d28f-cac9-48a4-90ff-8939f280e3ae_terseLabel_en-US" xlink:label="lab_us-gaap_OtherNoncurrentAssetsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other long-term assets, net [Member]</link:label>
    <link:label id="lab_us-gaap_OtherNoncurrentAssetsMember_label_en-US" xlink:label="lab_us-gaap_OtherNoncurrentAssetsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other Noncurrent Assets [Member]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherNoncurrentAssetsMember" xlink:to="lab_us-gaap_OtherNoncurrentAssetsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentIssuanceDate1_608b1b6e-a1db-4479-936f-00affdd04988_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentIssuanceDate1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Debt instrument, issuance date</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentIssuanceDate1" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_DebtInstrumentIssuanceDate1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentIssuanceDate1" xlink:to="lab_us-gaap_DebtInstrumentIssuanceDate1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ContractWithCustomerLiabilityRevenueRecognized_f2eeb1b8-10d2-4ca0-8ed9-5231a0ac7cbe_verboseLabel_en-US" xlink:label="lab_us-gaap_ContractWithCustomerLiabilityRevenueRecognized" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Transfer to revenues, including amounts reported in discontinued operations, contract liabilities</link:label>
    <link:label id="lab_us-gaap_ContractWithCustomerLiabilityRevenueRecognized_5f13c6db-9821-4237-8b7b-ac6008772a01_terseLabel_en-US" xlink:label="lab_us-gaap_ContractWithCustomerLiabilityRevenueRecognized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Revenue recognized</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractWithCustomerLiabilityRevenueRecognized" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_ContractWithCustomerLiabilityRevenueRecognized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ContractWithCustomerLiabilityRevenueRecognized" xlink:to="lab_us-gaap_ContractWithCustomerLiabilityRevenueRecognized" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract_fd08c114-3bb0-49e4-bf31-62adce9c8e38_terseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Commitments and Contingencies Disclosure [Abstract]</link:label>
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    <link:label id="lab_us-gaap_IncreaseDecreaseInInventories_633298f9-210e-4db2-9bce-f080e94292b3_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInInventories" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Decrease (increase) in inventories</link:label>
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    <link:label id="lab_us-gaap_DebtWeightedAverageInterestRate_c7a5965f-f589-4b6b-878f-883e008b4090_terseLabel_en-US" xlink:label="lab_us-gaap_DebtWeightedAverageInterestRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Weighted average interest rate</link:label>
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    <link:label id="lab_ns_GozoneBondsMember_documentation_en-US" xlink:label="lab_ns_GozoneBondsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">GoZone Bonds [Member]</link:label>
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    <link:label id="lab_us-gaap_DebtInstrumentAxis_7f17fd08-9cbe-47ed-b75e-f712cad465c4_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Debt Instrument [Axis]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentAxis_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Debt Instrument [Axis]</link:label>
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    <link:label id="lab_us-gaap_PartnerTypeOfPartnersCapitalAccountAxis_6984d7b3-2dad-46bb-84fc-30b4736af7a7_terseLabel_en-US" xlink:label="lab_us-gaap_PartnerTypeOfPartnersCapitalAccountAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Partner Type [Axis]</link:label>
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    <link:label id="lab_srt_CondensedFinancialStatementsCaptionsLineItems_d0b54c26-bb10-4f3b-aa81-3f48c4303be1_terseLabel_en-US" xlink:label="lab_srt_CondensedFinancialStatementsCaptionsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Condensed Financial Statements, Captions [Line Items]</link:label>
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    <link:label id="lab_us-gaap_OperatingSegmentsMember_963ab2a3-2a60-42f4-b64b-7c1db1702883_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingSegmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Total segment</link:label>
    <link:label id="lab_us-gaap_OperatingSegmentsMember_3bf0d6fb-0f7c-465f-b904-e30ab89a2929_verboseLabel_en-US" xlink:label="lab_us-gaap_OperatingSegmentsMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Total segment assets</link:label>
    <link:label id="lab_us-gaap_OperatingSegmentsMember_label_en-US" xlink:label="lab_us-gaap_OperatingSegmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Operating Segments [Member]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingSegmentsMember" xlink:to="lab_us-gaap_OperatingSegmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeCostOfHedgeNetOfCashReceived_31ff4ea2-336e-42e2-8536-80648b8bbf10_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeCostOfHedgeNetOfCashReceived" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Cash paid from termination of interest rate swaps</link:label>
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    <link:label id="lab_us-gaap_DisaggregationOfRevenueLineItems_44a5103a-ff75-4223-8718-42095656c473_terseLabel_en-US" xlink:label="lab_us-gaap_DisaggregationOfRevenueLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Disaggregation of Revenue [Line Items]</link:label>
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    <link:label id="lab_us-gaap_IncreaseDecreaseInAccruedLiabilities_084c10e1-1df4-4cf0-820a-f0701947845e_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccruedLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Increase (decrease) in accrued liabilities</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInAccruedLiabilities" xlink:to="lab_us-gaap_IncreaseDecreaseInAccruedLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfStockLineItems_1458248a-dafb-4e9d-a90c-cd0bbe8b45bb_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfStockLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Class of Stock [Line Items]</link:label>
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    <link:label id="lab_us-gaap_PartnersCapitalOther_28c8a9a1-74c8-46a4-a0a3-3bede3592c89_verboseLabel_en-US" xlink:label="lab_us-gaap_PartnersCapitalOther" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other</link:label>
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    <link:label id="lab_us-gaap_PartnersCapital_aaae2844-b59e-4f61-a0e7-16b52353a975_totalLabel_en-US" xlink:label="lab_us-gaap_PartnersCapital" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Total partners&#8217; equity</link:label>
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    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerAbstract_f7d5fa8e-fcc6-4b5b-94f4-d9ee3189dda1_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Revenue from Contract with Customer [Abstract]</link:label>
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    <link:label id="lab_ns_SharebasedPaymentArrangementAmortization_ed6eb07d-0f7c-4e24-99bc-3c9f39860990_terseLabel_en-US" xlink:label="lab_ns_SharebasedPaymentArrangementAmortization" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Amortization of unit-based compensation</link:label>
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    <link:label id="lab_ns_IntercompanyPayable_29a70dd1-d26c-459b-acc7-e41f2a8c212b_terseLabel_en-US" xlink:label="lab_ns_IntercompanyPayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Intercompany payable</link:label>
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    <link:label id="lab_ns_IntercompanyPayable_documentation_en-US" xlink:label="lab_ns_IntercompanyPayable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Payables between consolidated subsidiaries of the entity or between consolidated subsidiaries and the parent of the entity. These payables are eliminated when preparing consolidated financial statements.</link:label>
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    <link:label id="lab_us-gaap_EarningsPerLimitedPartnershipUnitAbstract_170deb41-8194-4623-b301-37fe98466e22_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerLimitedPartnershipUnitAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Basic net income (loss) per common unit</link:label>
    <link:label id="lab_us-gaap_EarningsPerLimitedPartnershipUnitAbstract_label_en-US" xlink:label="lab_us-gaap_EarningsPerLimitedPartnershipUnitAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net Income (Loss), Per Outstanding Limited Partnership Unit, Basic, Net of Tax [Abstract]</link:label>
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    <link:label id="lab_us-gaap_WeightedAverageNumerDilutedLimitedPartnershipUnitsOutstandingAdjustment_cb5727f8-4ca7-4ce2-9bf0-c38518fab190_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumerDilutedLimitedPartnershipUnitsOutstandingAdjustment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Effect of dilutive potential common units</link:label>
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    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_705deb75-ad7b-470c-a2b9-7dfde94b09bc_totalLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Income (loss) from continuing operations before income tax expense (benefit)</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Income (Loss) from Continuing Operations before Income Taxes, Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest"/>
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    <link:label id="lab_us-gaap_IncomeLossFromSubsidiariesBeforeTax_2ee3067a-fd13-4957-9867-f8ba2d88d632_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromSubsidiariesBeforeTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Equity in earnings (loss) of subsidiaries</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromSubsidiariesBeforeTax_label_en-US" xlink:label="lab_us-gaap_IncomeLossFromSubsidiariesBeforeTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Income (Loss) from Subsidiaries, before Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromSubsidiariesBeforeTax" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_IncomeLossFromSubsidiariesBeforeTax"/>
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    <link:label id="lab_us-gaap_OtherAssetImpairmentCharges_d14bb330-eb6d-4bbc-a7df-7c1697f5f09a_terseLabel_en-US" xlink:label="lab_us-gaap_OtherAssetImpairmentCharges" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Asset impairment losses</link:label>
    <link:label id="lab_us-gaap_OtherAssetImpairmentCharges_82e8bc7e-ce4e-40d4-8d23-a1fd8d995fbf_verboseLabel_en-US" xlink:label="lab_us-gaap_OtherAssetImpairmentCharges" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Asset impairment loss</link:label>
    <link:label id="lab_us-gaap_OtherAssetImpairmentCharges_label_en-US" xlink:label="lab_us-gaap_OtherAssetImpairmentCharges" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other Asset Impairment Charges</link:label>
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    <link:label id="lab_us-gaap_SubsequentEventMember_407e8d8b-1bf5-45bb-8596-cf5293936fec_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Subsequent Event [Member]</link:label>
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    <link:label id="lab_ns_UnsecuredTermLoanCreditAgreementMember_34bc830e-7757-4a34-9398-fb998c084ac3_terseLabel_en-US" xlink:label="lab_ns_UnsecuredTermLoanCreditAgreementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Unsecured Term Loan Credit Agreement [Member]</link:label>
    <link:label id="lab_ns_UnsecuredTermLoanCreditAgreementMember_label_en-US" xlink:label="lab_ns_UnsecuredTermLoanCreditAgreementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Unsecured Term Loan Credit Agreement [Member]</link:label>
    <link:label id="lab_ns_UnsecuredTermLoanCreditAgreementMember_documentation_en-US" xlink:label="lab_ns_UnsecuredTermLoanCreditAgreementMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Unsecured Term Loan Credit Agreement due 2023 [Member]</link:label>
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    <link:label id="lab_us-gaap_TemporaryEquityNetIncome_37d5825b-cd5e-41b2-849e-255389137765_verboseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityNetIncome" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net income, temporary equity</link:label>
    <link:label id="lab_us-gaap_TemporaryEquityNetIncome_label_en-US" xlink:label="lab_us-gaap_TemporaryEquityNetIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Temporary Equity, Net Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquityNetIncome" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_TemporaryEquityNetIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquityNetIncome" xlink:to="lab_us-gaap_TemporaryEquityNetIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PartnersCapitalNotesDisclosureTextBlock_d26ceca1-2b19-4021-8a84-0a5c12db1f72_terseLabel_en-US" xlink:label="lab_us-gaap_PartnersCapitalNotesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">PARTNERS' EQUITY</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PartnersCapitalNotesDisclosureTextBlock" xlink:to="lab_us-gaap_PartnersCapitalNotesDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LettersOfCreditOutstandingAmount_c3dc9c6d-20b2-4bac-9cbf-0d81c5cac49d_terseLabel_en-US" xlink:label="lab_us-gaap_LettersOfCreditOutstandingAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Letters of credit outstanding, amount</link:label>
    <link:label id="lab_us-gaap_LettersOfCreditOutstandingAmount_label_en-US" xlink:label="lab_us-gaap_LettersOfCreditOutstandingAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Letters of Credit Outstanding, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LettersOfCreditOutstandingAmount" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_LettersOfCreditOutstandingAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LettersOfCreditOutstandingAmount" xlink:to="lab_us-gaap_LettersOfCreditOutstandingAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DistributionMadeToLimitedPartnerDateOfRecord_97a7916b-78a8-4833-b7a8-a3d8478eccd1_verboseLabel_en-US" xlink:label="lab_us-gaap_DistributionMadeToLimitedPartnerDateOfRecord" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Distribution date of record</link:label>
    <link:label id="lab_us-gaap_DistributionMadeToLimitedPartnerDateOfRecord_label_en-US" xlink:label="lab_us-gaap_DistributionMadeToLimitedPartnerDateOfRecord" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Distribution Made to Limited Partner, Date of Record</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DistributionMadeToLimitedPartnerDateOfRecord" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_DistributionMadeToLimitedPartnerDateOfRecord"/>
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    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentGross_7c790ee6-8a38-4e29-86e3-105cf3c42a9f_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Property, plant and equipment, at cost</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentGross_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Property, Plant and Equipment, Gross</link:label>
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    <link:label id="lab_ns_PreferredLimitedPartnerMember_ab2e3159-6f86-4421-948c-fd31ed37db7d_terseLabel_en-US" xlink:label="lab_ns_PreferredLimitedPartnerMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred Limited Partner [Member]</link:label>
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    <link:label id="lab_dei_LegalEntityAxis_80977cb0-bcd1-45f4-8abf-6c13fe7f334a_terseLabel_en-US" xlink:label="lab_dei_LegalEntityAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Legal Entity [Axis]</link:label>
    <link:label id="lab_dei_LegalEntityAxis_label_en-US" xlink:label="lab_dei_LegalEntityAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Legal Entity [Axis]</link:label>
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    <link:label id="lab_dei_CityAreaCode_f53a8bde-aa37-4202-af96-5535e3a365c5_terseLabel_en-US" xlink:label="lab_dei_CityAreaCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">City Area Code</link:label>
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    <link:label id="lab_srt_ConsolidationItemsDomain_12eb2cb3-78fa-425a-8a50-86eaf4d48b57_terseLabel_en-US" xlink:label="lab_srt_ConsolidationItemsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Consolidation Items [Domain]</link:label>
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    <link:label id="lab_srt_NonGuarantorSubsidiariesMember_ec5a832c-1d31-41c2-9c6c-79ed8eee9f6c_terseLabel_en-US" xlink:label="lab_srt_NonGuarantorSubsidiariesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Non-Guarantor Subsidiaries [Member]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_srt_NonGuarantorSubsidiariesMember" xlink:href="http://xbrl.fasb.org/srt/2020/elts/srt-2020-01-31.xsd#srt_NonGuarantorSubsidiariesMember"/>
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    <link:label id="lab_dei_DocumentPeriodEndDate_32b50c44-eb45-4596-80f7-49b7ad8b631f_terseLabel_en-US" xlink:label="lab_dei_DocumentPeriodEndDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Document Period End Date</link:label>
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    <link:label id="lab_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionLineItems_37e99834-d1d8-49cb-8089-546014fcb47e_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Revenue, Remaining Performance Obligation, Expected Timing of Satisfaction [Line Items]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionLineItems" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionLineItems"/>
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    <link:loc xlink:type="locator" xlink:label="loc_srt_ScheduleOfCondensedFinancialStatementsTable" xlink:href="http://xbrl.fasb.org/srt/2020/elts/srt-2020-01-31.xsd#srt_ScheduleOfCondensedFinancialStatementsTable"/>
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    <link:label id="lab_us-gaap_PartnersCapitalAccountDistributions_b2faa128-a59d-47fa-8d6f-f7987f510209_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PartnersCapitalAccountDistributions" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Cash distributions to partners</link:label>
    <link:label id="lab_us-gaap_PartnersCapitalAccountDistributions_869d658d-9663-4424-9e73-62d6de51f08b_terseLabel_en-US" xlink:label="lab_us-gaap_PartnersCapitalAccountDistributions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fixed distribution per quarter</link:label>
    <link:label id="lab_us-gaap_PartnersCapitalAccountDistributions_label_en-US" xlink:label="lab_us-gaap_PartnersCapitalAccountDistributions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Partners' Capital Account, Distributions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PartnersCapitalAccountDistributions" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_PartnersCapitalAccountDistributions"/>
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    <link:label id="lab_us-gaap_LossContingencyAccrualAtCarryingValue_a5a83e69-8a47-4c1e-a4f9-142306e0829e_terseLabel_en-US" xlink:label="lab_us-gaap_LossContingencyAccrualAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Loss contingency accrual, at carrying value</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LossContingencyAccrualAtCarryingValue" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_LossContingencyAccrualAtCarryingValue"/>
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    <link:label id="lab_us-gaap_DisaggregationOfRevenueTableTextBlock_9e43af19-7a05-4e6c-aa7b-16851fec8541_terseLabel_en-US" xlink:label="lab_us-gaap_DisaggregationOfRevenueTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Disaggregation of Revenue [Table Text Block]</link:label>
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    <link:label id="lab_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTax_2fd153b2-bd1b-4637-8428-77077b537bb8_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTax" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net (gain) loss reclassified from AOCI</link:label>
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    <link:label id="lab_ns_LogisticsNotesDue2030Member_a7e0add2-ddfb-49d0-9c6f-b40ae4ebf081_terseLabel_en-US" xlink:label="lab_ns_LogisticsNotesDue2030Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Logistics Notes due 2030 [Member]</link:label>
    <link:label id="lab_ns_LogisticsNotesDue2030Member_label_en-US" xlink:label="lab_ns_LogisticsNotesDue2030Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Logistics Notes due 2030 [Member]</link:label>
    <link:label id="lab_ns_LogisticsNotesDue2030Member_documentation_en-US" xlink:label="lab_ns_LogisticsNotesDue2030Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Logistics 6.375% Notes due October 1, 2030</link:label>
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    <link:label id="lab_us-gaap_HedgingDesignationAxis_30869a5c-39c2-4c6b-acda-01c9fdadeb17_terseLabel_en-US" xlink:label="lab_us-gaap_HedgingDesignationAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Hedging Designation [Axis]</link:label>
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    <link:label id="lab_us-gaap_OtherIncomeMember_07a7cb0f-770e-471b-a2fd-482eb41c875a_terseLabel_en-US" xlink:label="lab_us-gaap_OtherIncomeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other income, net</link:label>
    <link:label id="lab_us-gaap_OtherIncomeMember_label_en-US" xlink:label="lab_us-gaap_OtherIncomeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other Income [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherIncomeMember" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_OtherIncomeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherIncomeMember" xlink:to="lab_us-gaap_OtherIncomeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionDescription_1af0cd55-a9a6-4661-8d63-0f2495bc4717_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionDescription" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Debt instrument, redemption, description</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionDescription_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionDescription" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Debt Instrument, Redemption, Description</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentRedemptionDescription" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_DebtInstrumentRedemptionDescription"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentRedemptionDescription" xlink:to="lab_us-gaap_DebtInstrumentRedemptionDescription" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquireProductiveAssets_2f371b96-9a0f-4e33-adee-9d7c4a6ae3dc_negatedLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireProductiveAssets" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Capital expenditures</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireProductiveAssets_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireProductiveAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Payments to Acquire Productive Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireProductiveAssets" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_PaymentsToAcquireProductiveAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquireProductiveAssets" xlink:to="lab_us-gaap_PaymentsToAcquireProductiveAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_ns_UnamortizedDebtIssuanceCostsUnamortizedDiscountAndCommitmentFeeMember_6f4042af-2258-4b28-9d70-f1c279fb6ab8_terseLabel_en-US" xlink:label="lab_ns_UnamortizedDebtIssuanceCostsUnamortizedDiscountAndCommitmentFeeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Unamortized Debt Issuance Costs, Unamortized Discount, and Commitment Fee [Member]</link:label>
    <link:label id="lab_ns_UnamortizedDebtIssuanceCostsUnamortizedDiscountAndCommitmentFeeMember_label_en-US" xlink:label="lab_ns_UnamortizedDebtIssuanceCostsUnamortizedDiscountAndCommitmentFeeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Unamortized Debt Issuance Costs, Unamortized Discount, and Commitment Fee [Member]</link:label>
    <link:label id="lab_ns_UnamortizedDebtIssuanceCostsUnamortizedDiscountAndCommitmentFeeMember_documentation_en-US" xlink:label="lab_ns_UnamortizedDebtIssuanceCostsUnamortizedDiscountAndCommitmentFeeMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Unamortized debt issuance costs, unamortized discount, and commitment fee</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ns_UnamortizedDebtIssuanceCostsUnamortizedDiscountAndCommitmentFeeMember" xlink:href="ns-20200930.xsd#ns_UnamortizedDebtIssuanceCostsUnamortizedDiscountAndCommitmentFeeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ns_UnamortizedDebtIssuanceCostsUnamortizedDiscountAndCommitmentFeeMember" xlink:to="lab_ns_UnamortizedDebtIssuanceCostsUnamortizedDiscountAndCommitmentFeeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityDomain_ed3d4334-53e8-4189-8806-bfb4351db96a_terseLabel_en-US" xlink:label="lab_dei_EntityDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity [Domain]</link:label>
    <link:label id="lab_dei_EntityDomain_label_en-US" xlink:label="lab_dei_EntityDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityDomain" xlink:href="https://xbrl.sec.gov/dei/2020/dei-2020-01-31.xsd#dei_EntityDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityDomain" xlink:to="lab_dei_EntityDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInInterestPayableNet_8551d098-0804-458c-82d2-f286d30b29c3_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInInterestPayableNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Increase (decrease) in accrued interest payable</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInInterestPayableNet_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInInterestPayableNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Increase (Decrease) in Interest Payable, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInInterestPayableNet" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_IncreaseDecreaseInInterestPayableNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInInterestPayableNet" xlink:to="lab_us-gaap_IncreaseDecreaseInInterestPayableNet" xlink:type="arc" order="1"/>
    <link:label id="lab_ns_EarlyRepaymentPremiumsMember_837019b2-062b-4329-9fd0-317738247431_terseLabel_en-US" xlink:label="lab_ns_EarlyRepaymentPremiumsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Early repayment premiums [Member]</link:label>
    <link:label id="lab_ns_EarlyRepaymentPremiumsMember_label_en-US" xlink:label="lab_ns_EarlyRepaymentPremiumsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Early Repayment Premiums [Member]</link:label>
    <link:label id="lab_ns_EarlyRepaymentPremiumsMember_documentation_en-US" xlink:label="lab_ns_EarlyRepaymentPremiumsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Early repayment premiums</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ns_EarlyRepaymentPremiumsMember" xlink:href="ns-20200930.xsd#ns_EarlyRepaymentPremiumsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ns_EarlyRepaymentPremiumsMember" xlink:to="lab_ns_EarlyRepaymentPremiumsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities_da00f751-1811-4613-ad11-2c618643ac4e_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other, net</link:label>
    <link:label id="lab_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities_label_en-US" xlink:label="lab_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Proceeds from (Payments for) Other Financing Activities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_ProceedsFromPaymentsForOtherFinancingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities" xlink:to="lab_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation_e92db162-03c2-40d2-82cb-abdb46a5f6af_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Payment of tax withholding for unit-based compensation</link:label>
    <link:label id="lab_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation_label_en-US" xlink:label="lab_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Payment, Tax Withholding, Share-based Payment Arrangement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:to="lab_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:type="arc" order="1"/>
    <link:label id="lab_ns_PreferredLimitedPartnerDistribution_7be095e7-ef24-46bf-b204-1495ad54efd7_negatedTerseLabel_en-US" xlink:label="lab_ns_PreferredLimitedPartnerDistribution" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Distributions to preferred limited partners</link:label>
    <link:label id="lab_ns_PreferredLimitedPartnerDistribution_label_en-US" xlink:label="lab_ns_PreferredLimitedPartnerDistribution" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred Limited Partner Distribution</link:label>
    <link:label id="lab_ns_PreferredLimitedPartnerDistribution_documentation_en-US" xlink:label="lab_ns_PreferredLimitedPartnerDistribution" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Distribution amount earned during the period allocated to the preferred limited partners.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ns_PreferredLimitedPartnerDistribution" xlink:href="ns-20200930.xsd#ns_PreferredLimitedPartnerDistribution"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ns_PreferredLimitedPartnerDistribution" xlink:to="lab_ns_PreferredLimitedPartnerDistribution" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DesignatedAsHedgingInstrumentMember_419d5319-a1d2-40f8-90c7-fb791c5171f3_terseLabel_en-US" xlink:label="lab_us-gaap_DesignatedAsHedgingInstrumentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Designated as Hedging Instruments</link:label>
    <link:label id="lab_us-gaap_DesignatedAsHedgingInstrumentMember_label_en-US" xlink:label="lab_us-gaap_DesignatedAsHedgingInstrumentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Designated as Hedging Instrument [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DesignatedAsHedgingInstrumentMember" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_DesignatedAsHedgingInstrumentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DesignatedAsHedgingInstrumentMember" xlink:to="lab_us-gaap_DesignatedAsHedgingInstrumentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnsecuredDebt_e81ad4e3-fe8d-43e5-8af2-c4984d9cc0aa_terseLabel_en-US" xlink:label="lab_us-gaap_UnsecuredDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">The Term Loan, Initial Loan</link:label>
    <link:label id="lab_us-gaap_UnsecuredDebt_label_en-US" xlink:label="lab_us-gaap_UnsecuredDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Unsecured Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnsecuredDebt" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_UnsecuredDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnsecuredDebt" xlink:to="lab_us-gaap_UnsecuredDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CoverAbstract_232a6efc-4aa3-470c-b106-46e7b6889484_terseLabel_en-US" xlink:label="lab_dei_CoverAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Cover [Abstract]</link:label>
    <link:label id="lab_dei_CoverAbstract_label_en-US" xlink:label="lab_dei_CoverAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Cover [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CoverAbstract" xlink:href="https://xbrl.sec.gov/dei/2020/dei-2020-01-31.xsd#dei_CoverAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CoverAbstract" xlink:to="lab_dei_CoverAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ns_DebtExtinguishmentCostsTypeAxis_5573d86b-7147-4ab7-859a-8d0259b4c7fe_terseLabel_en-US" xlink:label="lab_ns_DebtExtinguishmentCostsTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Debt Extinguishment Costs, Type [Axis]</link:label>
    <link:label id="lab_ns_DebtExtinguishmentCostsTypeAxis_label_en-US" xlink:label="lab_ns_DebtExtinguishmentCostsTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Debt Extinguishment Costs, Type [Axis]</link:label>
    <link:label id="lab_ns_DebtExtinguishmentCostsTypeAxis_documentation_en-US" xlink:label="lab_ns_DebtExtinguishmentCostsTypeAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Debt extinguishment Costs, type</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ns_DebtExtinguishmentCostsTypeAxis" xlink:href="ns-20200930.xsd#ns_DebtExtinguishmentCostsTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ns_DebtExtinguishmentCostsTypeAxis" xlink:to="lab_ns_DebtExtinguishmentCostsTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ns_ProceedsFromPaymentsForOtherFinancingActivitiesCondensedFinancialStatements_7aff8978-fcad-41ba-b376-2b1a256e3141_terseLabel_en-US" xlink:label="lab_ns_ProceedsFromPaymentsForOtherFinancingActivitiesCondensedFinancialStatements" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other, net</link:label>
    <link:label id="lab_ns_ProceedsFromPaymentsForOtherFinancingActivitiesCondensedFinancialStatements_label_en-US" xlink:label="lab_ns_ProceedsFromPaymentsForOtherFinancingActivitiesCondensedFinancialStatements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Proceeds From (Payments For) Other Financing Activities, Condensed Financial Statements</link:label>
    <link:label id="lab_ns_ProceedsFromPaymentsForOtherFinancingActivitiesCondensedFinancialStatements_documentation_en-US" xlink:label="lab_ns_ProceedsFromPaymentsForOtherFinancingActivitiesCondensedFinancialStatements" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">The net cash proceeds from (payments for) other types of financing activities.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ns_ProceedsFromPaymentsForOtherFinancingActivitiesCondensedFinancialStatements" xlink:href="ns-20200930.xsd#ns_ProceedsFromPaymentsForOtherFinancingActivitiesCondensedFinancialStatements"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ns_ProceedsFromPaymentsForOtherFinancingActivitiesCondensedFinancialStatements" xlink:to="lab_ns_ProceedsFromPaymentsForOtherFinancingActivitiesCondensedFinancialStatements" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsNetOfTax_2808f26b-6200-4810-8a27-441fda63ea40_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsNetOfTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other comprehensive income (loss) before reclassification adjustments</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsNetOfTax_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other Comprehensive Income (Loss), before Reclassifications, Net of Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsNetOfTax" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsNetOfTax"/>
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    <link:label id="lab_ns_LogisticsNotesDue2025Member_documentation_en-US" xlink:label="lab_ns_LogisticsNotesDue2025Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Logistics 5.75% Notes due October 1, 2025</link:label>
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    <link:label id="lab_us-gaap_ContractWithCustomerAssetNetNoncurrent_3c656d34-5430-48b9-84ee-85e0b25da6a5_verboseLabel_en-US" xlink:label="lab_us-gaap_ContractWithCustomerAssetNetNoncurrent" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Noncurrent portion</link:label>
    <link:label id="lab_us-gaap_ContractWithCustomerAssetNetNoncurrent_label_en-US" xlink:label="lab_us-gaap_ContractWithCustomerAssetNetNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Contract with Customer, Asset, after Allowance for Credit Loss, Noncurrent</link:label>
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    <link:label id="lab_dei_EntityInteractiveDataCurrent_a6cb1761-02b2-4865-ae5e-cda6443501a3_terseLabel_en-US" xlink:label="lab_dei_EntityInteractiveDataCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Interactive Data Current</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityInteractiveDataCurrent" xlink:to="lab_dei_EntityInteractiveDataCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_ns_LiabilitiesHeldforSaleMember_12c678d8-fe13-49ac-9a8e-09ce17593cea_terseLabel_en-US" xlink:label="lab_ns_LiabilitiesHeldforSaleMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Liabilities held for sale</link:label>
    <link:label id="lab_ns_LiabilitiesHeldforSaleMember_label_en-US" xlink:label="lab_ns_LiabilitiesHeldforSaleMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Liabilities Held for Sale [Member]</link:label>
    <link:label id="lab_ns_LiabilitiesHeldforSaleMember_documentation_en-US" xlink:label="lab_ns_LiabilitiesHeldforSaleMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Liabilities of a component or group of components classified as held-for-sale and representing a strategic shift that has or will have a major effect on operations and financial results</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ns_LiabilitiesHeldforSaleMember" xlink:href="ns-20200930.xsd#ns_LiabilitiesHeldforSaleMember"/>
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    <link:label id="lab_us-gaap_IncreaseDecreaseInPartnersCapitalRollForward_bcfb2eda-15a8-496c-b71b-a0ad796fba86_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInPartnersCapitalRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Increase (Decrease) in Partners' Capital [Roll Forward]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInPartnersCapitalRollForward" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_IncreaseDecreaseInPartnersCapitalRollForward"/>
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    <link:label id="lab_us-gaap_RevenuesAbstract_edc2d837-336f-47b5-9da6-8666aa43a36c_terseLabel_en-US" xlink:label="lab_us-gaap_RevenuesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Revenues:</link:label>
    <link:label id="lab_us-gaap_RevenuesAbstract_label_en-US" xlink:label="lab_us-gaap_RevenuesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Revenues [Abstract]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenuesAbstract" xlink:to="lab_us-gaap_RevenuesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_b0db8731-05b2-4108-91d6-7efc6cd0f611_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Cash Flows from Operating Activities:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_80e75e92-f9ce-4937-8841-60ac072999a9_verboseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Cash flows from operating activities:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net Cash Provided by (Used in) Operating Activities [Abstract]</link:label>
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    <link:label id="lab_ns_ProceedsFromPaymentsForTerminationOfInterestRateSwaps_07fc6e19-6fa4-4478-b92b-aa4c5506bf99_negatedTerseLabel_en-US" xlink:label="lab_ns_ProceedsFromPaymentsForTerminationOfInterestRateSwaps" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Payments for termination of interest rate swaps</link:label>
    <link:label id="lab_ns_ProceedsFromPaymentsForTerminationOfInterestRateSwaps_label_en-US" xlink:label="lab_ns_ProceedsFromPaymentsForTerminationOfInterestRateSwaps" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Proceeds from (Payments for) Termination of Interest Rate Swaps</link:label>
    <link:label id="lab_ns_ProceedsFromPaymentsForTerminationOfInterestRateSwaps_documentation_en-US" xlink:label="lab_ns_ProceedsFromPaymentsForTerminationOfInterestRateSwaps" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Proceeds from (payments for) termination of interest rate swap agreements</link:label>
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    <link:label id="lab_ns_GoZoneBondsDueOctober2040Member_2acc652b-5b6c-489d-9387-f0595678ebcf_terseLabel_en-US" xlink:label="lab_ns_GoZoneBondsDueOctober2040Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">GoZone Bonds Due October 2040</link:label>
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    <link:label id="lab_ns_GoZoneBondsDueOctober2040Member_documentation_en-US" xlink:label="lab_ns_GoZoneBondsDueOctober2040Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">GoZone Bonds Due October 2040</link:label>
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    <link:label id="lab_srt_NameOfMajorCustomerDomain_1efd1baa-d2dc-473b-8d6a-e24116171849_terseLabel_en-US" xlink:label="lab_srt_NameOfMajorCustomerDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Customer [Domain]</link:label>
    <link:label id="lab_srt_NameOfMajorCustomerDomain_label_en-US" xlink:label="lab_srt_NameOfMajorCustomerDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Customer [Domain]</link:label>
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    <link:label id="lab_ns_OriginalIssueDiscount_61e54d78-659f-49c0-8727-5e0b78cfeb8d_terseLabel_en-US" xlink:label="lab_ns_OriginalIssueDiscount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Long-term debt, original issue discount, rate</link:label>
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    <link:label id="lab_ns_OriginalIssueDiscount_documentation_en-US" xlink:label="lab_ns_OriginalIssueDiscount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Original Issue Discount</link:label>
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    <link:label id="lab_us-gaap_UnusualOrInfrequentItemAxis_05e47a2e-7461-4f9c-ba33-b84e38a3b4f8_terseLabel_en-US" xlink:label="lab_us-gaap_UnusualOrInfrequentItemAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Unusual or Infrequent Item, or Both [Axis]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnusualOrInfrequentItemAxis" xlink:to="lab_us-gaap_UnusualOrInfrequentItemAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityRegistrantName_5e5a09f4-bbb1-4c47-96b2-1feaecec5ede_terseLabel_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Registrant Name</link:label>
    <link:label id="lab_dei_EntityRegistrantName_label_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Registrant Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityRegistrantName" xlink:href="https://xbrl.sec.gov/dei/2020/dei-2020-01-31.xsd#dei_EntityRegistrantName"/>
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    <link:label id="lab_ns_EpuDistributionsLessThanGreaterThanEarningsAllocatedToLimitedPartners_c86709f2-10e2-43c2-abe2-ee7543cc75ba_terseLabel_en-US" xlink:label="lab_ns_EpuDistributionsLessThanGreaterThanEarningsAllocatedToLimitedPartners" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Allocation of distributions in excess of loss</link:label>
    <link:label id="lab_ns_EpuDistributionsLessThanGreaterThanEarningsAllocatedToLimitedPartners_label_en-US" xlink:label="lab_ns_EpuDistributionsLessThanGreaterThanEarningsAllocatedToLimitedPartners" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">EPU Distributions Less Than Greater Than Earnings Allocated to Limited Partners</link:label>
    <link:label id="lab_ns_EpuDistributionsLessThanGreaterThanEarningsAllocatedToLimitedPartners_documentation_en-US" xlink:label="lab_ns_EpuDistributionsLessThanGreaterThanEarningsAllocatedToLimitedPartners" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Distributions less than or (greater than) earnings, allocated to the limited partners.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ns_EpuDistributionsLessThanGreaterThanEarningsAllocatedToLimitedPartners" xlink:href="ns-20200930.xsd#ns_EpuDistributionsLessThanGreaterThanEarningsAllocatedToLimitedPartners"/>
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    <link:label id="lab_us-gaap_SubsequentEventTypeDomain_075396e8-e628-44bf-8651-dd810382d18a_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Subsequent Event Type [Domain]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventTypeDomain_label_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Subsequent Event Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventTypeDomain" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_SubsequentEventTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventTypeDomain" xlink:to="lab_us-gaap_SubsequentEventTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingInformationRevenueAbstract_c0d9fcbd-cfb6-4b5c-99da-cf35da14c67b_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingInformationRevenueAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Revenues:</link:label>
    <link:label id="lab_us-gaap_SegmentReportingInformationRevenueAbstract_label_en-US" xlink:label="lab_us-gaap_SegmentReportingInformationRevenueAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Segment Reporting Information, Revenue for Reportable Segment [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingInformationRevenueAbstract" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_SegmentReportingInformationRevenueAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingInformationRevenueAbstract" xlink:to="lab_us-gaap_SegmentReportingInformationRevenueAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetImpairmentCharges_08a153c4-96f2-42d6-9750-8e4e4b1cc501_terseLabel_en-US" xlink:label="lab_us-gaap_AssetImpairmentCharges" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Asset and goodwill impairment losses</link:label>
    <link:label id="lab_us-gaap_AssetImpairmentCharges_label_en-US" xlink:label="lab_us-gaap_AssetImpairmentCharges" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Asset Impairment Charges</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetImpairmentCharges" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_AssetImpairmentCharges"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetImpairmentCharges" xlink:to="lab_us-gaap_AssetImpairmentCharges" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IntersegmentEliminationMember_2f4176ea-0dff-4aad-a4cb-356c7f27b509_terseLabel_en-US" xlink:label="lab_us-gaap_IntersegmentEliminationMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Intersegment Eliminations [Member]</link:label>
    <link:label id="lab_us-gaap_IntersegmentEliminationMember_label_en-US" xlink:label="lab_us-gaap_IntersegmentEliminationMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Intersegment Eliminations [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IntersegmentEliminationMember" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_IntersegmentEliminationMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IntersegmentEliminationMember" xlink:to="lab_us-gaap_IntersegmentEliminationMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NumberOfReportableSegments_29f956fc-603b-4f81-b8fe-0bd98ac87d50_terseLabel_en-US" xlink:label="lab_us-gaap_NumberOfReportableSegments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Number of business segments</link:label>
    <link:label id="lab_us-gaap_NumberOfReportableSegments_label_en-US" xlink:label="lab_us-gaap_NumberOfReportableSegments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Number of Reportable Segments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NumberOfReportableSegments" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_NumberOfReportableSegments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NumberOfReportableSegments" xlink:to="lab_us-gaap_NumberOfReportableSegments" xlink:type="arc" order="1"/>
    <link:label id="lab_ns_CrudeOilPipelinesMember_48d37b1e-da3e-4634-9b67-a7273d25a291_terseLabel_en-US" xlink:label="lab_ns_CrudeOilPipelinesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Crude Oil Pipelines [Member]</link:label>
    <link:label id="lab_ns_CrudeOilPipelinesMember_label_en-US" xlink:label="lab_ns_CrudeOilPipelinesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Crude Oil Pipelines [Member]</link:label>
    <link:label id="lab_ns_CrudeOilPipelinesMember_documentation_en-US" xlink:label="lab_ns_CrudeOilPipelinesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Crude Oil Pipelines</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ns_CrudeOilPipelinesMember" xlink:href="ns-20200930.xsd#ns_CrudeOilPipelinesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ns_CrudeOilPipelinesMember" xlink:to="lab_ns_CrudeOilPipelinesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsOfDividendsCommonStock_7db334be-7b74-4391-a987-2650aa03affe_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsOfDividendsCommonStock" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Distributions to common unitholders</link:label>
    <link:label id="lab_us-gaap_PaymentsOfDividendsCommonStock_label_en-US" xlink:label="lab_us-gaap_PaymentsOfDividendsCommonStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Payments of Ordinary Dividends, Common Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsOfDividendsCommonStock" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_PaymentsOfDividendsCommonStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsOfDividendsCommonStock" xlink:to="lab_us-gaap_PaymentsOfDividendsCommonStock" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ConsolidationItemsAxis_a7481d66-8ae4-46c8-89fa-9f43d183b0f7_terseLabel_en-US" xlink:label="lab_srt_ConsolidationItemsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Consolidation Items [Axis]</link:label>
    <link:label id="lab_srt_ConsolidationItemsAxis_label_en-US" xlink:label="lab_srt_ConsolidationItemsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Consolidation Items [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidationItemsAxis" xlink:href="http://xbrl.fasb.org/srt/2020/elts/srt-2020-01-31.xsd#srt_ConsolidationItemsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ConsolidationItemsAxis" xlink:to="lab_srt_ConsolidationItemsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccruedLiabilitiesMember_ce4932a8-c077-46ac-8e70-abddaddf5c18_terseLabel_en-US" xlink:label="lab_us-gaap_AccruedLiabilitiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accrued liabilities</link:label>
    <link:label id="lab_us-gaap_AccruedLiabilitiesMember_label_en-US" xlink:label="lab_us-gaap_AccruedLiabilitiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accrued Liabilities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccruedLiabilitiesMember" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_AccruedLiabilitiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccruedLiabilitiesMember" xlink:to="lab_us-gaap_AccruedLiabilitiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityIncorporationStateCountryCode_541eace9-b684-4454-82f2-66d0dba1d3a6_terseLabel_en-US" xlink:label="lab_dei_EntityIncorporationStateCountryCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Incorporation, State or Country Code</link:label>
    <link:label id="lab_dei_EntityIncorporationStateCountryCode_label_en-US" xlink:label="lab_dei_EntityIncorporationStateCountryCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Incorporation, State or Country Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityIncorporationStateCountryCode" xlink:href="https://xbrl.sec.gov/dei/2020/dei-2020-01-31.xsd#dei_EntityIncorporationStateCountryCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityIncorporationStateCountryCode" xlink:to="lab_dei_EntityIncorporationStateCountryCode" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GoodwillImpairmentLoss_0992a547-3882-46ca-b77c-40c0a786f78e_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillImpairmentLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Goodwill impairment loss</link:label>
    <link:label id="lab_us-gaap_GoodwillImpairmentLoss_label_en-US" xlink:label="lab_us-gaap_GoodwillImpairmentLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Goodwill, Impairment Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillImpairmentLoss" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_GoodwillImpairmentLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillImpairmentLoss" xlink:to="lab_us-gaap_GoodwillImpairmentLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsReceivableNetCurrent_f1fbde25-0493-4fe2-951d-d09aee9c6572_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsReceivableNetCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accounts receivable, net</link:label>
    <link:label id="lab_us-gaap_AccountsReceivableNetCurrent_label_en-US" xlink:label="lab_us-gaap_AccountsReceivableNetCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accounts Receivable, after Allowance for Credit Loss, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsReceivableNetCurrent" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_AccountsReceivableNetCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsReceivableNetCurrent" xlink:to="lab_us-gaap_AccountsReceivableNetCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DividendsPreferredStockCash_54e50db9-f45c-461d-816b-745bac243860_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DividendsPreferredStockCash" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Cash distributions to partners, temporary equity</link:label>
    <link:label id="lab_us-gaap_DividendsPreferredStockCash_label_en-US" xlink:label="lab_us-gaap_DividendsPreferredStockCash" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Dividends, Preferred Stock, Cash</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DividendsPreferredStockCash" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_DividendsPreferredStockCash"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DividendsPreferredStockCash" xlink:to="lab_us-gaap_DividendsPreferredStockCash" xlink:type="arc" order="1"/>
    <link:label id="lab_ns_NustarPipelineOperatingPartnershipLpMember_0173eac1-152c-4c2c-89c0-0147c4339b9c_terseLabel_en-US" xlink:label="lab_ns_NustarPipelineOperatingPartnershipLpMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">NuPOP</link:label>
    <link:label id="lab_ns_NustarPipelineOperatingPartnershipLpMember_label_en-US" xlink:label="lab_ns_NustarPipelineOperatingPartnershipLpMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">NuStar Pipeline Operating Partnership LP [Member]</link:label>
    <link:label id="lab_ns_NustarPipelineOperatingPartnershipLpMember_documentation_en-US" xlink:label="lab_ns_NustarPipelineOperatingPartnershipLpMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">NuStar Pipeline Operating Partnership L.P. [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ns_NustarPipelineOperatingPartnershipLpMember" xlink:href="ns-20200930.xsd#ns_NustarPipelineOperatingPartnershipLpMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ns_NustarPipelineOperatingPartnershipLpMember" xlink:to="lab_ns_NustarPipelineOperatingPartnershipLpMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ns_LogisticsNotesDue2020Member_e1b5b6d9-190e-44ba-9d14-ba9904d5e157_terseLabel_en-US" xlink:label="lab_ns_LogisticsNotesDue2020Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Logistics Notes due 2020 [Member]</link:label>
    <link:label id="lab_ns_LogisticsNotesDue2020Member_label_en-US" xlink:label="lab_ns_LogisticsNotesDue2020Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Logistics Notes due 2020 [Member]</link:label>
    <link:label id="lab_ns_LogisticsNotesDue2020Member_documentation_en-US" xlink:label="lab_ns_LogisticsNotesDue2020Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Logistics 4.80% Notes due September 2020</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ns_LogisticsNotesDue2020Member" xlink:href="ns-20200930.xsd#ns_LogisticsNotesDue2020Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ns_LogisticsNotesDue2020Member" xlink:to="lab_ns_LogisticsNotesDue2020Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PartnersCapitalAccountUnitBasedCompensation_f84d54fc-322d-4f78-a26d-dc6a8bf9d577_terseLabel_en-US" xlink:label="lab_us-gaap_PartnersCapitalAccountUnitBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Unit-based compensation</link:label>
    <link:label id="lab_us-gaap_PartnersCapitalAccountUnitBasedCompensation_label_en-US" xlink:label="lab_us-gaap_PartnersCapitalAccountUnitBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Partners' Capital Account, Unit-based Payment Arrangement, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PartnersCapitalAccountUnitBasedCompensation" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_PartnersCapitalAccountUnitBasedCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PartnersCapitalAccountUnitBasedCompensation" xlink:to="lab_us-gaap_PartnersCapitalAccountUnitBasedCompensation" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_OtherComprehensiveIncomeMember_89ba3d99-b5db-4ea7-93c6-73733b25dfbc_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other comprehensive income</link:label>
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    <link:label id="lab_us-gaap_Goodwill_d39245b7-0f3c-4faa-a10d-1a63b96cce8e_terseLabel_en-US" xlink:label="lab_us-gaap_Goodwill" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Goodwill</link:label>
    <link:label id="lab_us-gaap_Goodwill_label_en-US" xlink:label="lab_us-gaap_Goodwill" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Goodwill</link:label>
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    <link:label id="lab_ns_MezzanineEquityDisclosureTextBlock_817f80f3-3ad3-4036-8f86-b7a25282cd29_terseLabel_en-US" xlink:label="lab_ns_MezzanineEquityDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">SERIES D CUMULATIVE COVERTIBLE PREFERRED UNITS</link:label>
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    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent_70a185aa-07ce-41ac-b9aa-fdce38894535_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other comprehensive income (loss)</link:label>
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    <link:label id="lab_srt_GuarantorSubsidiariesMember_29a6115f-0a9d-4b38-a76e-ca86a8a131ec_terseLabel_en-US" xlink:label="lab_srt_GuarantorSubsidiariesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Guarantor Subsidiaries [Member]</link:label>
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    <link:label id="lab_dei_DocumentTransitionReport_3aa980c6-196a-4956-8d92-7c9bb7245795_terseLabel_en-US" xlink:label="lab_dei_DocumentTransitionReport" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Document Transition Report</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentTransitionReport" xlink:to="lab_dei_DocumentTransitionReport" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel2Member_4ebccf73-f2ea-4ae8-ab0d-97231d2656de_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel2Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fair Value, Inputs, Level 2 [Member]</link:label>
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    <link:label id="lab_ns_ScheduleOfGoZoneBondsTableTextBlock_0bbaa58f-276c-446e-9b68-942c6b0b7c4b_terseLabel_en-US" xlink:label="lab_ns_ScheduleOfGoZoneBondsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Schedule of GoZone Bonds</link:label>
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    <link:label id="lab_ns_SeriesBPreferredLimitedPartnerMember_63171633-cbd3-4628-ad9a-5f6e116042a3_terseLabel_en-US" xlink:label="lab_ns_SeriesBPreferredLimitedPartnerMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Series B Preferred Limited Partner [Member]</link:label>
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    <link:label id="lab_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock_5a8bb2cd-f432-47f5-8397-32f5666e37fc_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">IMPAIRMENTS AND DISCONTINUED OPERATIONS</link:label>
    <link:label id="lab_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Disposal Groups, Including Discontinued Operations, Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock" xlink:to="lab_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeFixedInterestRate_99b6ab5d-8879-4043-931b-487dfbcc2bff_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeFixedInterestRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Interest rate swaps, interest rate paid</link:label>
    <link:label id="lab_us-gaap_DerivativeFixedInterestRate_label_en-US" xlink:label="lab_us-gaap_DerivativeFixedInterestRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative, Fixed Interest Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeFixedInterestRate" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_DerivativeFixedInterestRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeFixedInterestRate" xlink:to="lab_us-gaap_DerivativeFixedInterestRate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ContractWithCustomerLiabilityCurrent_940deb6b-a980-4f74-b13b-448618cb4eff_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_ContractWithCustomerLiabilityCurrent" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Current portion/Held for sale</link:label>
    <link:label id="lab_us-gaap_ContractWithCustomerLiabilityCurrent_label_en-US" xlink:label="lab_us-gaap_ContractWithCustomerLiabilityCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Contract with Customer, Liability, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractWithCustomerLiabilityCurrent" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_ContractWithCustomerLiabilityCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ContractWithCustomerLiabilityCurrent" xlink:to="lab_us-gaap_ContractWithCustomerLiabilityCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtTerm_76317b38-ef4d-4e0a-9789-9f8ade595c2c_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtTerm" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Long-term debt, term</link:label>
    <link:label id="lab_us-gaap_LongTermDebtTerm_label_en-US" xlink:label="lab_us-gaap_LongTermDebtTerm" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Long-term Debt, Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtTerm" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_LongTermDebtTerm"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtTerm" xlink:to="lab_us-gaap_LongTermDebtTerm" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventLineItems_1f6adf9b-55ec-4401-a247-7d3e38e058d5_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Subsequent Event [Line Items]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventLineItems_label_en-US" xlink:label="lab_us-gaap_SubsequentEventLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Subsequent Event [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventLineItems" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_SubsequentEventLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventLineItems" xlink:to="lab_us-gaap_SubsequentEventLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RepaymentsOfShortTermDebt_2cb703c0-2bf9-49dd-9340-d57ef9dfa0c7_negatedLabel_en-US" xlink:label="lab_us-gaap_RepaymentsOfShortTermDebt" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Short-term debt repayments</link:label>
    <link:label id="lab_us-gaap_RepaymentsOfShortTermDebt_label_en-US" xlink:label="lab_us-gaap_RepaymentsOfShortTermDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Repayments of Short-term Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RepaymentsOfShortTermDebt" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_RepaymentsOfShortTermDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RepaymentsOfShortTermDebt" xlink:to="lab_us-gaap_RepaymentsOfShortTermDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NewAccountingPronouncementsAndChangesInAccountingPrinciplesTextBlock_068e9385-197f-45ff-92bd-83ed287bbd57_terseLabel_en-US" xlink:label="lab_us-gaap_NewAccountingPronouncementsAndChangesInAccountingPrinciplesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">NEW ACCOUNTING PRONOUNCEMENTS</link:label>
    <link:label id="lab_us-gaap_NewAccountingPronouncementsAndChangesInAccountingPrinciplesTextBlock_label_en-US" xlink:label="lab_us-gaap_NewAccountingPronouncementsAndChangesInAccountingPrinciplesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accounting Standards Update and Change in Accounting Principle [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NewAccountingPronouncementsAndChangesInAccountingPrinciplesTextBlock" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_NewAccountingPronouncementsAndChangesInAccountingPrinciplesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NewAccountingPronouncementsAndChangesInAccountingPrinciplesTextBlock" xlink:to="lab_us-gaap_NewAccountingPronouncementsAndChangesInAccountingPrinciplesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeContractTypeDomain_f16d1f97-21b3-417e-8a81-50d3d09c36b2_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeContractTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative Contract [Domain]</link:label>
    <link:label id="lab_us-gaap_DerivativeContractTypeDomain_label_en-US" xlink:label="lab_us-gaap_DerivativeContractTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative Contract [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeContractTypeDomain" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_DerivativeContractTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeContractTypeDomain" xlink:to="lab_us-gaap_DerivativeContractTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityFileNumber_d2f1b33a-bc7f-4064-972d-da21c8c9eb9e_terseLabel_en-US" xlink:label="lab_dei_EntityFileNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity File Number</link:label>
    <link:label id="lab_dei_EntityFileNumber_label_en-US" xlink:label="lab_dei_EntityFileNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity File Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFileNumber" xlink:href="https://xbrl.sec.gov/dei/2020/dei-2020-01-31.xsd#dei_EntityFileNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityFileNumber" xlink:to="lab_dei_EntityFileNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherCurrentLiabilitiesMember_09210aac-ad79-4c10-a151-3ea198c069ad_terseLabel_en-US" xlink:label="lab_us-gaap_OtherCurrentLiabilitiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accrued Liabilities [Member]</link:label>
    <link:label id="lab_us-gaap_OtherCurrentLiabilitiesMember_label_en-US" xlink:label="lab_us-gaap_OtherCurrentLiabilitiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other Current Liabilities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherCurrentLiabilitiesMember" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_OtherCurrentLiabilitiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherCurrentLiabilitiesMember" xlink:to="lab_us-gaap_OtherCurrentLiabilitiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtDisclosureAbstract_cf1b913c-9fac-44b3-958d-2ec8976790ab_terseLabel_en-US" xlink:label="lab_us-gaap_DebtDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Debt Disclosure [Abstract]</link:label>
    <link:label id="lab_us-gaap_DebtDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_DebtDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Debt Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtDisclosureAbstract" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_DebtDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtDisclosureAbstract" xlink:to="lab_us-gaap_DebtDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccrualForTaxesOtherThanIncomeTaxesCurrent_92f5bf2f-c5d0-47ca-be68-be2a9071926f_terseLabel_en-US" xlink:label="lab_us-gaap_AccrualForTaxesOtherThanIncomeTaxesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Taxes other than income tax</link:label>
    <link:label id="lab_us-gaap_AccrualForTaxesOtherThanIncomeTaxesCurrent_label_en-US" xlink:label="lab_us-gaap_AccrualForTaxesOtherThanIncomeTaxesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accrual for Taxes Other than Income Taxes, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccrualForTaxesOtherThanIncomeTaxesCurrent" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_AccrualForTaxesOtherThanIncomeTaxesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccrualForTaxesOtherThanIncomeTaxesCurrent" xlink:to="lab_us-gaap_AccrualForTaxesOtherThanIncomeTaxesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_ns_IncreaseDecreaseinAccountsPayableRelatedtoCapitalExpenditures_14e723ad-2bef-4582-87e6-bee2bce55ead_terseLabel_en-US" xlink:label="lab_ns_IncreaseDecreaseinAccountsPayableRelatedtoCapitalExpenditures" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Change in accounts payable related to capital expenditures</link:label>
    <link:label id="lab_ns_IncreaseDecreaseinAccountsPayableRelatedtoCapitalExpenditures_label_en-US" xlink:label="lab_ns_IncreaseDecreaseinAccountsPayableRelatedtoCapitalExpenditures" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Increase (Decrease) in Accounts Payable Related to Capital Expenditures</link:label>
    <link:label id="lab_ns_IncreaseDecreaseinAccountsPayableRelatedtoCapitalExpenditures_documentation_en-US" xlink:label="lab_ns_IncreaseDecreaseinAccountsPayableRelatedtoCapitalExpenditures" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">The increase (decrease) in accounts payable related to capital expenditures that have been incurred but not yet paid.</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ns_IncreaseDecreaseinAccountsPayableRelatedtoCapitalExpenditures" xlink:to="lab_ns_IncreaseDecreaseinAccountsPayableRelatedtoCapitalExpenditures" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RepaymentsOfLongTermDebt_0a93f330-a8aa-42be-89d2-8b5e9e1cb695_terseLabel_en-US" xlink:label="lab_us-gaap_RepaymentsOfLongTermDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Amount repaid</link:label>
    <link:label id="lab_us-gaap_RepaymentsOfLongTermDebt_label_en-US" xlink:label="lab_us-gaap_RepaymentsOfLongTermDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Repayments of Long-term Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RepaymentsOfLongTermDebt" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_RepaymentsOfLongTermDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RepaymentsOfLongTermDebt" xlink:to="lab_us-gaap_RepaymentsOfLongTermDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_c389f3cd-a98f-4195-8b2b-aaf165da3694_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net cash (used in) provided by financing activities</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueRemainingPerformanceObligation_c38fbe2a-f484-459b-b77b-07ead85f93a9_verboseLabel_en-US" xlink:label="lab_us-gaap_RevenueRemainingPerformanceObligation" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Revenue, remaining performance obligation, amount</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueRemainingPerformanceObligation" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_RevenueRemainingPerformanceObligation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenueRemainingPerformanceObligation" xlink:to="lab_us-gaap_RevenueRemainingPerformanceObligation" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_DebtInstrumentCollateralAmount_a69ceff3-ce1b-4acf-bd7b-2f9005dfeb47_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentCollateralAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Debt instrument, collateral amount</link:label>
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    <link:label id="lab_us-gaap_OtherDepreciationAndAmortization_26d3cccd-c6f9-4f68-8bc9-75347e66aeb1_verboseLabel_en-US" xlink:label="lab_us-gaap_OtherDepreciationAndAmortization" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other depreciation and amortization expense</link:label>
    <link:label id="lab_us-gaap_OtherDepreciationAndAmortization_label_en-US" xlink:label="lab_us-gaap_OtherDepreciationAndAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other Depreciation and Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherDepreciationAndAmortization" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_OtherDepreciationAndAmortization"/>
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    <link:label id="lab_us-gaap_PaymentsOfDividendsPreferredStockAndPreferenceStock_aeab3795-dd5a-436a-8918-21e74d46850a_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsOfDividendsPreferredStockAndPreferenceStock" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Distributions to preferred unitholders</link:label>
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    <link:label id="lab_us-gaap_BalanceSheetLocationAxis_bdc83e5a-868b-46d6-ad83-bbc38c2d0b42_terseLabel_en-US" xlink:label="lab_us-gaap_BalanceSheetLocationAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Balance Sheet Location [Axis]</link:label>
    <link:label id="lab_us-gaap_BalanceSheetLocationAxis_label_en-US" xlink:label="lab_us-gaap_BalanceSheetLocationAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Balance Sheet Location [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BalanceSheetLocationAxis" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_BalanceSheetLocationAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BalanceSheetLocationAxis" xlink:to="lab_us-gaap_BalanceSheetLocationAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ns_EPUCommonLimitedPartnerAllocation_ea2e09d8-d4bd-405d-9c17-d9833a820214_terseLabel_en-US" xlink:label="lab_ns_EPUCommonLimitedPartnerAllocation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net (loss) income attributable to common units</link:label>
    <link:label id="lab_ns_EPUCommonLimitedPartnerAllocation_label_en-US" xlink:label="lab_ns_EPUCommonLimitedPartnerAllocation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">EPU Common Limited Partner Allocation</link:label>
    <link:label id="lab_ns_EPUCommonLimitedPartnerAllocation_documentation_en-US" xlink:label="lab_ns_EPUCommonLimitedPartnerAllocation" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Allocation of distributed and undistributed earnings (loss) to the common limited partners in the EPU calculation.</link:label>
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    <link:label id="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsAxis_8daaf914-c898-46ab-beeb-36707124dd85_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Disposal Group Name [Axis]</link:label>
    <link:label id="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsAxis_label_en-US" xlink:label="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Disposal Group Name [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsAxis" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsAxis"/>
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    <link:label id="lab_dei_DocumentFiscalYearFocus_b37c2ed0-6b96-4cb5-beaf-3ac222862394_terseLabel_en-US" xlink:label="lab_dei_DocumentFiscalYearFocus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Document Fiscal Year Focus</link:label>
    <link:label id="lab_dei_DocumentFiscalYearFocus_label_en-US" xlink:label="lab_dei_DocumentFiscalYearFocus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Document Fiscal Year Focus</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentFiscalYearFocus" xlink:href="https://xbrl.sec.gov/dei/2020/dei-2020-01-31.xsd#dei_DocumentFiscalYearFocus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentFiscalYearFocus" xlink:to="lab_dei_DocumentFiscalYearFocus" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtCurrent_484dd6d6-88fc-443c-999f-0d162cfe8e7e_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Current portion of long-term debt</link:label>
    <link:label id="lab_us-gaap_LongTermDebtCurrent_label_en-US" xlink:label="lab_us-gaap_LongTermDebtCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Long-term Debt, Current Maturities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtCurrent" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_LongTermDebtCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtCurrent" xlink:to="lab_us-gaap_LongTermDebtCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCurrentReportingStatus_4d3439e9-264c-478f-8b52-057c32f4849c_terseLabel_en-US" xlink:label="lab_dei_EntityCurrentReportingStatus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Current Reporting Status</link:label>
    <link:label id="lab_dei_EntityCurrentReportingStatus_label_en-US" xlink:label="lab_dei_EntityCurrentReportingStatus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Current Reporting Status</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCurrentReportingStatus" xlink:href="https://xbrl.sec.gov/dei/2020/dei-2020-01-31.xsd#dei_EntityCurrentReportingStatus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCurrentReportingStatus" xlink:to="lab_dei_EntityCurrentReportingStatus" xlink:type="arc" order="1"/>
    <link:label id="lab_ns_GoZoneBondsDueJune2038Member_9acab458-e269-4269-82db-8081bfbf86a1_terseLabel_en-US" xlink:label="lab_ns_GoZoneBondsDueJune2038Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">GoZone Bonds Due June 2038</link:label>
    <link:label id="lab_ns_GoZoneBondsDueJune2038Member_label_en-US" xlink:label="lab_ns_GoZoneBondsDueJune2038Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">GoZone Bonds Due June 2038 [Member]</link:label>
    <link:label id="lab_ns_GoZoneBondsDueJune2038Member_documentation_en-US" xlink:label="lab_ns_GoZoneBondsDueJune2038Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">$55.4 million GoZone Bonds Due June 2038</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ns_GoZoneBondsDueJune2038Member" xlink:href="ns-20200930.xsd#ns_GoZoneBondsDueJune2038Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ns_GoZoneBondsDueJune2038Member" xlink:to="lab_ns_GoZoneBondsDueJune2038Member" xlink:type="arc" order="1"/>
    <link:label id="lab_ns_DiscontinuedOperationsSelectedCashFlowInformationTableTextBlock_1ec19e73-a787-47d4-a983-5b7b15daa0f4_verboseLabel_en-US" xlink:label="lab_ns_DiscontinuedOperationsSelectedCashFlowInformationTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Discontinued Operations, Selected Cash Flow Information</link:label>
    <link:label id="lab_ns_DiscontinuedOperationsSelectedCashFlowInformationTableTextBlock_label_en-US" xlink:label="lab_ns_DiscontinuedOperationsSelectedCashFlowInformationTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Discontinued Operations, Selected Cash Flow Information [Table Text Block]</link:label>
    <link:label id="lab_ns_DiscontinuedOperationsSelectedCashFlowInformationTableTextBlock_documentation_en-US" xlink:label="lab_ns_DiscontinuedOperationsSelectedCashFlowInformationTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Discontinued Operations, Selected Cash Flow Information [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ns_DiscontinuedOperationsSelectedCashFlowInformationTableTextBlock" xlink:href="ns-20200930.xsd#ns_DiscontinuedOperationsSelectedCashFlowInformationTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ns_DiscontinuedOperationsSelectedCashFlowInformationTableTextBlock" xlink:to="lab_ns_DiscontinuedOperationsSelectedCashFlowInformationTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ns_ContributionsFromDistributionsToAffiliates_bffba1b0-31cc-446a-8838-7add970673f6_terseLabel_en-US" xlink:label="lab_ns_ContributionsFromDistributionsToAffiliates" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Contributions from (distributions to) affiliates</link:label>
    <link:label id="lab_ns_ContributionsFromDistributionsToAffiliates_label_en-US" xlink:label="lab_ns_ContributionsFromDistributionsToAffiliates" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Contributions From Distributions To Affiliates</link:label>
    <link:label id="lab_ns_ContributionsFromDistributionsToAffiliates_documentation_en-US" xlink:label="lab_ns_ContributionsFromDistributionsToAffiliates" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Contributions from (distributions to) subsidiaries and/or parent</link:label>
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    <link:label id="lab_ns_GoZoneBondsDueJuly2040Member_9fd4a55c-9f47-48ed-99f5-6faae276b125_terseLabel_en-US" xlink:label="lab_ns_GoZoneBondsDueJuly2040Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">GoZone Bonds Due July 2040</link:label>
    <link:label id="lab_ns_GoZoneBondsDueJuly2040Member_label_en-US" xlink:label="lab_ns_GoZoneBondsDueJuly2040Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">GoZone Bonds Due July 2040 [Member]</link:label>
    <link:label id="lab_ns_GoZoneBondsDueJuly2040Member_documentation_en-US" xlink:label="lab_ns_GoZoneBondsDueJuly2040Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">$100.0 million GoZone Bonds Due July 2040</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ns_GoZoneBondsDueJuly2040Member" xlink:href="ns-20200930.xsd#ns_GoZoneBondsDueJuly2040Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ns_GoZoneBondsDueJuly2040Member" xlink:to="lab_ns_GoZoneBondsDueJuly2040Member" xlink:type="arc" order="1"/>
    <link:label id="lab_ns_AmendedReceivablesFinancingAgreementMember_08d07b92-2317-4cea-8524-1336b8830ce6_terseLabel_en-US" xlink:label="lab_ns_AmendedReceivablesFinancingAgreementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Receivables Financing Agreement [Member]</link:label>
    <link:label id="lab_ns_AmendedReceivablesFinancingAgreementMember_label_en-US" xlink:label="lab_ns_AmendedReceivablesFinancingAgreementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Amended Receivables Financing Agreement [Member]</link:label>
    <link:label id="lab_ns_AmendedReceivablesFinancingAgreementMember_documentation_en-US" xlink:label="lab_ns_AmendedReceivablesFinancingAgreementMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">$125.0 million NuStar Energy L.P. and NuStar Finance LLC receivables financing agreement due 2021 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ns_AmendedReceivablesFinancingAgreementMember" xlink:href="ns-20200930.xsd#ns_AmendedReceivablesFinancingAgreementMember"/>
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    <link:label id="lab_us-gaap_SubsequentEventTable_c2740624-efab-47d5-820c-c659c4c71aa9_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Subsequent Event [Table]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventTable" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_SubsequentEventTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventTable" xlink:to="lab_us-gaap_SubsequentEventTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativesAndFairValueTextBlock_5ed28f3b-ff68-4a0d-91b0-d3901cbd9010_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativesAndFairValueTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">DERIVATIVES AND FAIR VALUE MEASUREMENTS</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativesAndFairValueTextBlock" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_DerivativesAndFairValueTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativesAndFairValueTextBlock" xlink:to="lab_us-gaap_DerivativesAndFairValueTextBlock" xlink:type="arc" order="1"/>
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    <link:label id="lab_ns_TheSt.EustatiusDispositionMember_label_en-US" xlink:label="lab_ns_TheSt.EustatiusDispositionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">The St. Eustatius Disposition [Member]</link:label>
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    <link:label id="lab_us-gaap_SegmentReportingAbstract_290e7353-4dd8-42bb-8c75-5d932e69a5fc_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Segment Reporting [Abstract]</link:label>
    <link:label id="lab_us-gaap_SegmentReportingAbstract_label_en-US" xlink:label="lab_us-gaap_SegmentReportingAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Segment Reporting [Abstract]</link:label>
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    <link:label id="lab_us-gaap_InterestExpenseMember_94f581e3-73df-4ed4-b9d0-4b56cdd6f6f6_terseLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Interest expense, net</link:label>
    <link:label id="lab_us-gaap_InterestExpenseMember_label_en-US" xlink:label="lab_us-gaap_InterestExpenseMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Interest Expense [Member]</link:label>
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    <link:label id="lab_us-gaap_IncreaseDecreaseInAccountsReceivable_12b0b470-d8e7-4b56-aa24-88447cb61990_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Decrease (increase) in accounts receivable</link:label>
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    <link:label id="lab_us-gaap_DebtInstrumentLineItems_8cbaaf8a-d7ec-4e51-a3f8-211cf4b9b5b9_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Debt Instrument [Line Items]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentLineItems" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_DebtInstrumentLineItems"/>
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    <link:label id="lab_us-gaap_TemporaryEquityCarryingAmountAttributableToParent_label_en-US" xlink:label="lab_us-gaap_TemporaryEquityCarryingAmountAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Temporary Equity, Carrying Amount, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquityCarryingAmountAttributableToParent" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_TemporaryEquityCarryingAmountAttributableToParent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquityCarryingAmountAttributableToParent" xlink:to="lab_us-gaap_TemporaryEquityCarryingAmountAttributableToParent" xlink:type="arc" order="1"/>
    <link:label id="lab_ns_ChangeinContractwithCustomerAssetTotal_130e5aec-dfa1-47aa-9a54-e0de0dff0c5e_totalLabel_en-US" xlink:label="lab_ns_ChangeinContractwithCustomerAssetTotal" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Total activity</link:label>
    <link:label id="lab_ns_ChangeinContractwithCustomerAssetTotal_label_en-US" xlink:label="lab_ns_ChangeinContractwithCustomerAssetTotal" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Change in Contract with Customer, Asset, Total</link:label>
    <link:label id="lab_ns_ChangeinContractwithCustomerAssetTotal_documentation_en-US" xlink:label="lab_ns_ChangeinContractwithCustomerAssetTotal" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Total change in contract with customer asset balance in the current period.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ns_ChangeinContractwithCustomerAssetTotal" xlink:href="ns-20200930.xsd#ns_ChangeinContractwithCustomerAssetTotal"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ns_ChangeinContractwithCustomerAssetTotal" xlink:to="lab_ns_ChangeinContractwithCustomerAssetTotal" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquity_d4953b12-f200-4f7e-b1e8-94de1347b50a_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Total liabilities, mezzanine equity and partners&#8217; equity</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquity_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Liabilities and Equity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAndStockholdersEquity" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_LiabilitiesAndStockholdersEquity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesAndStockholdersEquity" xlink:to="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:type="arc" order="1"/>
    <link:label id="lab_ns_CommonLimitedPartnerMember_5bfa2ff0-a49a-4fd7-8a2b-e3f08dfa324a_terseLabel_en-US" xlink:label="lab_ns_CommonLimitedPartnerMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Common Limited Partner [Member]</link:label>
    <link:label id="lab_ns_CommonLimitedPartnerMember_label_en-US" xlink:label="lab_ns_CommonLimitedPartnerMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Common Limited Partner [Member]</link:label>
    <link:label id="lab_ns_CommonLimitedPartnerMember_documentation_en-US" xlink:label="lab_ns_CommonLimitedPartnerMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Partner with ownership interests in the issuer that is subordinate to the preferred limited partner.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ns_CommonLimitedPartnerMember" xlink:href="ns-20200930.xsd#ns_CommonLimitedPartnerMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ns_CommonLimitedPartnerMember" xlink:to="lab_ns_CommonLimitedPartnerMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationGeneralAndAdministrativeExpense_0fa3294a-59c2-466d-aa00-17bdbf27de84_verboseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationGeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">General and administrative expenses (excluding depreciation and amortization expense)</link:label>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationGeneralAndAdministrativeExpense_label_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationGeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Disposal Group, Including Discontinued Operation, General and Administrative Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationGeneralAndAdministrativeExpense" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationGeneralAndAdministrativeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationGeneralAndAdministrativeExpense" xlink:to="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationGeneralAndAdministrativeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RepaymentsOfOtherLongTermDebt_988387dd-1779-4405-a7a5-2c625e85d3c4_negatedLabel_en-US" xlink:label="lab_us-gaap_RepaymentsOfOtherLongTermDebt" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other long-term debt repayments</link:label>
    <link:label id="lab_us-gaap_RepaymentsOfOtherLongTermDebt_label_en-US" xlink:label="lab_us-gaap_RepaymentsOfOtherLongTermDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Repayments of Other Long-term Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RepaymentsOfOtherLongTermDebt" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_RepaymentsOfOtherLongTermDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RepaymentsOfOtherLongTermDebt" xlink:to="lab_us-gaap_RepaymentsOfOtherLongTermDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_8b8c8ac9-9437-4698-9db7-3576d5b77cc9_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accumulated other comprehensive loss</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_bba04b67-9cf3-4a5c-82b1-1ea579a16c9c_periodStartLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Beginning balance</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_37917972-23fd-4934-bdaa-0384190c11b0_periodEndLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Ending balance</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss), Net of Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:to="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressCityOrTown_e6af4582-0f6c-428e-bc97-ab3845e8e689_terseLabel_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Address, City</link:label>
    <link:label id="lab_dei_EntityAddressCityOrTown_label_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Address, City or Town</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressCityOrTown" xlink:href="https://xbrl.sec.gov/dei/2020/dei-2020-01-31.xsd#dei_EntityAddressCityOrTown"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressCityOrTown" xlink:to="lab_dei_EntityAddressCityOrTown" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReconciliationOfAssetsFromSegmentToConsolidatedTable_3ca40a9e-ca6a-428e-bb8a-e544f089c476_terseLabel_en-US" xlink:label="lab_us-gaap_ReconciliationOfAssetsFromSegmentToConsolidatedTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Reconciliation of Assets from Segment to Consolidated [Table]</link:label>
    <link:label id="lab_us-gaap_ReconciliationOfAssetsFromSegmentToConsolidatedTable_label_en-US" xlink:label="lab_us-gaap_ReconciliationOfAssetsFromSegmentToConsolidatedTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Reconciliation of Assets from Segment to Consolidated [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReconciliationOfAssetsFromSegmentToConsolidatedTable" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_ReconciliationOfAssetsFromSegmentToConsolidatedTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReconciliationOfAssetsFromSegmentToConsolidatedTable" xlink:to="lab_us-gaap_ReconciliationOfAssetsFromSegmentToConsolidatedTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis_913eaf5a-df42-45ca-8dfc-c7c4fe6abe51_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fair Value Hierarchy and NAV [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fair Value Hierarchy and NAV [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_FairValueByFairValueHierarchyLevelAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:to="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ns_ContractwithCustomerAssetAdditions_3cd9f693-2c98-4d1a-b0f5-daae894fca9a_terseLabel_en-US" xlink:label="lab_ns_ContractwithCustomerAssetAdditions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Additions</link:label>
    <link:label id="lab_ns_ContractwithCustomerAssetAdditions_label_en-US" xlink:label="lab_ns_ContractwithCustomerAssetAdditions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Contract with Customer, Asset, Additions</link:label>
    <link:label id="lab_ns_ContractwithCustomerAssetAdditions_documentation_en-US" xlink:label="lab_ns_ContractwithCustomerAssetAdditions" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Contract with Customer, Asset, Additions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ns_ContractwithCustomerAssetAdditions" xlink:href="ns-20200930.xsd#ns_ContractwithCustomerAssetAdditions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ns_ContractwithCustomerAssetAdditions" xlink:to="lab_ns_ContractwithCustomerAssetAdditions" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ParentMember_5ead2adf-61f7-42c1-8192-21b00db4170e_verboseLabel_en-US" xlink:label="lab_us-gaap_ParentMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_ParentMember_label_en-US" xlink:label="lab_us-gaap_ParentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Parent [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ParentMember" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_ParentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ParentMember" xlink:to="lab_us-gaap_ParentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis_1e5aa710-f555-48eb-bf67-830307ba19ec_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Hedging Relationship [Axis]</link:label>
    <link:label id="lab_us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Hedging Relationship [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis" xlink:to="lab_us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GeneralAndAdministrativeExpense_0130a918-3754-4f9c-8fcf-166569d24cbb_verboseLabel_en-US" xlink:label="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">General and administrative expenses (excluding depreciation and amortization expense)</link:label>
    <link:label id="lab_us-gaap_GeneralAndAdministrativeExpense_5a7f2bac-6a61-4090-8f0a-57a23048098f_terseLabel_en-US" xlink:label="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">General and administrative expenses</link:label>
    <link:label id="lab_us-gaap_GeneralAndAdministrativeExpense_label_en-US" xlink:label="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">General and Administrative Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GeneralAndAdministrativeExpense" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_GeneralAndAdministrativeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GeneralAndAdministrativeExpense" xlink:to="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_ns_PartnersCapitalandTemporaryEquity_43bc767b-103a-45c0-8111-ba4a6cd0889b_periodStartLabel_en-US" xlink:label="lab_ns_PartnersCapitalandTemporaryEquity" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Partners' capital and temporary equity - beginning balance</link:label>
    <link:label id="lab_ns_PartnersCapitalandTemporaryEquity_6b3831a2-a293-4802-a24e-4a93f09f3d74_periodEndLabel_en-US" xlink:label="lab_ns_PartnersCapitalandTemporaryEquity" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Partners' capital and temporary equity - ending balance</link:label>
    <link:label id="lab_ns_PartnersCapitalandTemporaryEquity_label_en-US" xlink:label="lab_ns_PartnersCapitalandTemporaryEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Partners' Capital and Temporary Equity</link:label>
    <link:label id="lab_ns_PartnersCapitalandTemporaryEquity_documentation_en-US" xlink:label="lab_ns_PartnersCapitalandTemporaryEquity" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Partners' capital and temporary equity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ns_PartnersCapitalandTemporaryEquity" xlink:href="ns-20200930.xsd#ns_PartnersCapitalandTemporaryEquity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ns_PartnersCapitalandTemporaryEquity" xlink:to="lab_ns_PartnersCapitalandTemporaryEquity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherNoncashIncomeExpense_7bdab015-19b2-4234-a45c-f5b176a64ee1_negatedLabel_en-US" xlink:label="lab_us-gaap_OtherNoncashIncomeExpense" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other, net</link:label>
    <link:label id="lab_us-gaap_OtherNoncashIncomeExpense_label_en-US" xlink:label="lab_us-gaap_OtherNoncashIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other Noncash Income (Expense)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherNoncashIncomeExpense" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_OtherNoncashIncomeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherNoncashIncomeExpense" xlink:to="lab_us-gaap_OtherNoncashIncomeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProductMember_824a14b4-b24e-424b-a66a-1389e6d605b0_terseLabel_en-US" xlink:label="lab_us-gaap_ProductMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Product [Member]</link:label>
    <link:label id="lab_us-gaap_ProductMember_label_en-US" xlink:label="lab_us-gaap_ProductMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Product [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProductMember" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_ProductMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProductMember" xlink:to="lab_us-gaap_ProductMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityComponentDomain_e4aa04fa-bddc-4774-a578-c47edba9ad8d_terseLabel_en-US" xlink:label="lab_us-gaap_EquityComponentDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Equity Component [Domain]</link:label>
    <link:label id="lab_us-gaap_EquityComponentDomain_label_en-US" xlink:label="lab_us-gaap_EquityComponentDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Equity Component [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityComponentDomain" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_EquityComponentDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityComponentDomain" xlink:to="lab_us-gaap_EquityComponentDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxPerOutstandingLimitedPartnershipUnitDiluted1_9f204131-f163-4d53-9c5b-a5262adc4950_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxPerOutstandingLimitedPartnershipUnitDiluted1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Discontinued operations</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxPerOutstandingLimitedPartnershipUnitDiluted1_label_en-US" xlink:label="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxPerOutstandingLimitedPartnershipUnitDiluted1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Income (Loss) from Discontinued Operations, Net of Tax, Per Outstanding Limited Partnership Unit, Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxPerOutstandingLimitedPartnershipUnitDiluted1" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxPerOutstandingLimitedPartnershipUnitDiluted1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxPerOutstandingLimitedPartnershipUnitDiluted1" xlink:to="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxPerOutstandingLimitedPartnershipUnitDiluted1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherNoncurrentAssets_f226dbfa-4c3b-4bac-916e-b20c46195a3a_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherNoncurrentAssets" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">(Increase) decrease in other long-term assets</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherNoncurrentAssets_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherNoncurrentAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Increase (Decrease) in Other Noncurrent Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOtherNoncurrentAssets" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_IncreaseDecreaseInOtherNoncurrentAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOtherNoncurrentAssets" xlink:to="lab_us-gaap_IncreaseDecreaseInOtherNoncurrentAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_ns_PipelineSegmentMember_c1938e4a-a4dd-40b5-97e8-e4cfd4109c99_terseLabel_en-US" xlink:label="lab_ns_PipelineSegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Pipeline Segment</link:label>
    <link:label id="lab_ns_PipelineSegmentMember_label_en-US" xlink:label="lab_ns_PipelineSegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Pipeline Segment [Member]</link:label>
    <link:label id="lab_ns_PipelineSegmentMember_documentation_en-US" xlink:label="lab_ns_PipelineSegmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Segment of the business engaged in the transportation of products</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ns_PipelineSegmentMember" xlink:href="ns-20200930.xsd#ns_PipelineSegmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ns_PipelineSegmentMember" xlink:to="lab_ns_PipelineSegmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentNet_ac276d98-ae09-4d94-a7fe-eaa1933b85b6_totalLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Property, plant and equipment, net</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentNet_33bf261c-803c-4055-8aae-21de1d3dbd71_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Property, plant and equipment, net</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentNet_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Property, Plant and Equipment, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentNet" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_PropertyPlantAndEquipmentNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentNet" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentNet" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ReportableLegalEntitiesMember_35913a23-09d8-48b0-9b75-9279bb410816_terseLabel_en-US" xlink:label="lab_srt_ReportableLegalEntitiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Reportable Legal Entities [Member]</link:label>
    <link:label id="lab_srt_ReportableLegalEntitiesMember_label_en-US" xlink:label="lab_srt_ReportableLegalEntitiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Reportable Legal Entities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ReportableLegalEntitiesMember" xlink:href="http://xbrl.fasb.org/srt/2020/elts/srt-2020-01-31.xsd#srt_ReportableLegalEntitiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ReportableLegalEntitiesMember" xlink:to="lab_srt_ReportableLegalEntitiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityTaxIdentificationNumber_ea0f71c9-2737-42aa-867c-80e15774f1cb_terseLabel_en-US" xlink:label="lab_dei_EntityTaxIdentificationNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Tax Identification Number</link:label>
    <link:label id="lab_dei_EntityTaxIdentificationNumber_label_en-US" xlink:label="lab_dei_EntityTaxIdentificationNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Tax Identification Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityTaxIdentificationNumber" xlink:href="https://xbrl.sec.gov/dei/2020/dei-2020-01-31.xsd#dei_EntityTaxIdentificationNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityTaxIdentificationNumber" xlink:to="lab_dei_EntityTaxIdentificationNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestIncomeExpenseNonoperatingNet_34f22c23-074d-4a22-b109-ed81827e5528_terseLabel_en-US" xlink:label="lab_us-gaap_InterestIncomeExpenseNonoperatingNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Interest expense, net</link:label>
    <link:label id="lab_us-gaap_InterestIncomeExpenseNonoperatingNet_fb7da7a0-bd95-4f1e-a6f0-ad570b919f78_verboseLabel_en-US" xlink:label="lab_us-gaap_InterestIncomeExpenseNonoperatingNet" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Interest income (expense), net</link:label>
    <link:label id="lab_us-gaap_InterestIncomeExpenseNonoperatingNet_label_en-US" xlink:label="lab_us-gaap_InterestIncomeExpenseNonoperatingNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Interest Income (Expense), Nonoperating, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestIncomeExpenseNonoperatingNet" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_InterestIncomeExpenseNonoperatingNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestIncomeExpenseNonoperatingNet" xlink:to="lab_us-gaap_InterestIncomeExpenseNonoperatingNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestRateContractMember_7f3e9f97-bd21-40ef-a818-64be4ca77b3f_terseLabel_en-US" xlink:label="lab_us-gaap_InterestRateContractMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Interest rate swaps</link:label>
    <link:label id="lab_us-gaap_InterestRateContractMember_label_en-US" xlink:label="lab_us-gaap_InterestRateContractMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Interest Rate Contract [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestRateContractMember" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_InterestRateContractMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestRateContractMember" xlink:to="lab_us-gaap_InterestRateContractMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLoss_3578630c-7c8a-479b-81be-e95a8f110e74_totalLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net (loss) income</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_d7f947ba-edf9-4524-98b0-6ad3f6068a95_verboseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net income (loss)</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_709d64a3-ba6a-4b43-9117-6e5815e7e4d8_terseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net income (loss)</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_label_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net Income (Loss) Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLoss" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_NetIncomeLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLoss" xlink:to="lab_us-gaap_NetIncomeLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherCurrentAssetsAndLiabilitiesNet_31789f20-d035-450f-8f49-d0789be7a289_negatedLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherCurrentAssetsAndLiabilitiesNet" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Changes in current assets and current liabilities (Note 11)</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherCurrentAssetsAndLiabilitiesNet_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherCurrentAssetsAndLiabilitiesNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Increase (Decrease) in Other Current Assets and Liabilities, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOtherCurrentAssetsAndLiabilitiesNet" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_IncreaseDecreaseInOtherCurrentAssetsAndLiabilitiesNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOtherCurrentAssetsAndLiabilitiesNet" xlink:to="lab_us-gaap_IncreaseDecreaseInOtherCurrentAssetsAndLiabilitiesNet" xlink:type="arc" order="1"/>
    <link:label id="lab_ns_DerivativeNotionalAmountTerminated_ebe1ba26-6f69-48f2-bb30-8c5e9a1a5660_terseLabel_en-US" xlink:label="lab_ns_DerivativeNotionalAmountTerminated" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Notional amount of forward-starting interest rate swaps terminated</link:label>
    <link:label id="lab_ns_DerivativeNotionalAmountTerminated_label_en-US" xlink:label="lab_ns_DerivativeNotionalAmountTerminated" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative, Notional Amount, Terminated</link:label>
    <link:label id="lab_ns_DerivativeNotionalAmountTerminated_documentation_en-US" xlink:label="lab_ns_DerivativeNotionalAmountTerminated" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Aggregate notional amount that was terminated, specified by the derivative(s).</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ns_DerivativeNotionalAmountTerminated" xlink:href="ns-20200930.xsd#ns_DerivativeNotionalAmountTerminated"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ns_DerivativeNotionalAmountTerminated" xlink:to="lab_ns_DerivativeNotionalAmountTerminated" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsCurrent_1a1459cb-d53e-46e9-88e1-e3018ab241ba_totalLabel_en-US" xlink:label="lab_us-gaap_AssetsCurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Total current assets</link:label>
    <link:label id="lab_us-gaap_AssetsCurrent_label_en-US" xlink:label="lab_us-gaap_AssetsCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Assets, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsCurrent" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_AssetsCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsCurrent" xlink:to="lab_us-gaap_AssetsCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CurrentFiscalYearEndDate_dae08d99-0ae7-4237-bc15-0d54d7078122_terseLabel_en-US" xlink:label="lab_dei_CurrentFiscalYearEndDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Current Fiscal Year End Date</link:label>
    <link:label id="lab_dei_CurrentFiscalYearEndDate_label_en-US" xlink:label="lab_dei_CurrentFiscalYearEndDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Current Fiscal Year End Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CurrentFiscalYearEndDate" xlink:href="https://xbrl.sec.gov/dei/2020/dei-2020-01-31.xsd#dei_CurrentFiscalYearEndDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CurrentFiscalYearEndDate" xlink:to="lab_dei_CurrentFiscalYearEndDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareAbstract_5b4b7a3c-2d65-425b-8d0c-c82d77a31b74_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Earnings Per Share [Abstract]</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareAbstract_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Earnings Per Share [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareAbstract" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_EarningsPerShareAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareAbstract" xlink:to="lab_us-gaap_EarningsPerShareAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInPropertyAndOtherTaxesPayable_a43b3eb0-6788-4626-8397-313534905805_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInPropertyAndOtherTaxesPayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Increase (decrease) in taxes other than income tax</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInPropertyAndOtherTaxesPayable_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInPropertyAndOtherTaxesPayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Increase (Decrease) in Property and Other Taxes Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInPropertyAndOtherTaxesPayable" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_IncreaseDecreaseInPropertyAndOtherTaxesPayable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInPropertyAndOtherTaxesPayable" xlink:to="lab_us-gaap_IncreaseDecreaseInPropertyAndOtherTaxesPayable" xlink:type="arc" order="1"/>
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    <link:label id="lab_ns_NustarLogisticsLpMember_be865351-5ab6-4351-a330-c6fc19acb579_terseLabel_en-US" xlink:label="lab_ns_NustarLogisticsLpMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">NuStar Logistics</link:label>
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    <link:label id="lab_us-gaap_PreferredStockDividendPaymentRateVariable_1b86e2ec-40e5-4340-8c74-de481537ea20_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockDividendPaymentRateVariable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred units, dividend payment rate, variable</link:label>
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    <link:label id="lab_us-gaap_CashFlowOperatingCapitalTableTextBlock_ad0d9b80-a434-414f-b6dc-a8bd3cb374dd_terseLabel_en-US" xlink:label="lab_us-gaap_CashFlowOperatingCapitalTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Schedule of Changes in Current Assets and Liabilities [Table Text Block]</link:label>
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    <link:label id="lab_us-gaap_UnusualOrInfrequentItemDomain_089aaef4-9c19-4f1e-9d43-008c04b506a6_terseLabel_en-US" xlink:label="lab_us-gaap_UnusualOrInfrequentItemDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Unusual or Infrequent Item, or Both [Domain]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnusualOrInfrequentItemDomain" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_UnusualOrInfrequentItemDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnusualOrInfrequentItemDomain" xlink:to="lab_us-gaap_UnusualOrInfrequentItemDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage_730c6af8-55f4-4656-b706-419c1a94ca98_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Long-term debt, rate</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Debt Instrument, Interest Rate, Stated Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_DebtInstrumentInterestRateStatedPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:to="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionPeriod1_18b596b2-f48e-49d9-8453-5bb2fb7e3e9e_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionPeriod1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Revenue, remaining performance obligation, expected timing of satisfaction, period</link:label>
    <link:label id="lab_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionPeriod1_label_en-US" xlink:label="lab_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionPeriod1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Revenue, Remaining Performance Obligation, Expected Timing of Satisfaction, Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionPeriod1" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionPeriod1"/>
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    <link:label id="lab_ns_DepreciationDepletionAndAmortizationFromContinuingAndDiscontinuedOperations_5f05c325-57f9-4442-b995-0b486d8a2371_terseLabel_en-US" xlink:label="lab_ns_DepreciationDepletionAndAmortizationFromContinuingAndDiscontinuedOperations" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Depreciation and amortization expense</link:label>
    <link:label id="lab_ns_DepreciationDepletionAndAmortizationFromContinuingAndDiscontinuedOperations_label_en-US" xlink:label="lab_ns_DepreciationDepletionAndAmortizationFromContinuingAndDiscontinuedOperations" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Depreciation, Depletion and Amortization, From Continuing and Discontinued Operations</link:label>
    <link:label id="lab_ns_DepreciationDepletionAndAmortizationFromContinuingAndDiscontinuedOperations_documentation_en-US" xlink:label="lab_ns_DepreciationDepletionAndAmortizationFromContinuingAndDiscontinuedOperations" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">The aggregate expense recognized in the current period that allocates the cost of tangible assets, intangible assets, or depleting assets to periods that benefit from use of the assets. Includes expense included in continuing and discontinued operations.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ns_DepreciationDepletionAndAmortizationFromContinuingAndDiscontinuedOperations" xlink:href="ns-20200930.xsd#ns_DepreciationDepletionAndAmortizationFromContinuingAndDiscontinuedOperations"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ns_DepreciationDepletionAndAmortizationFromContinuingAndDiscontinuedOperations" xlink:to="lab_ns_DepreciationDepletionAndAmortizationFromContinuingAndDiscontinuedOperations" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_4f17fbe4-c9ba-4d9c-b5d3-0ca1034210e6_negatedLabel_en-US" xlink:label="lab_us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accumulated depreciation and amortization</link:label>
    <link:label id="lab_us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_label_en-US" xlink:label="lab_us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accumulated Depreciation, Depletion and Amortization, Property, Plant, and Equipment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment" xlink:to="lab_us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ContractWithCustomerAssetNetCurrent_81292f1d-638e-4dee-b326-442bc42a23b0_verboseLabel_en-US" xlink:label="lab_us-gaap_ContractWithCustomerAssetNetCurrent" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Current portion/Held for sale</link:label>
    <link:label id="lab_us-gaap_ContractWithCustomerAssetNetCurrent_label_en-US" xlink:label="lab_us-gaap_ContractWithCustomerAssetNetCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Contract with Customer, Asset, after Allowance for Credit Loss, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractWithCustomerAssetNetCurrent" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_ContractWithCustomerAssetNetCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ContractWithCustomerAssetNetCurrent" xlink:to="lab_us-gaap_ContractWithCustomerAssetNetCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfSubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipTable_a16a8eec-54c5-4dea-90bf-21f2d953a20a_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfSubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Schedule of Subsidiary of Limited Liability Company or Limited Partnership [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfSubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfSubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Schedule of Subsidiary of Limited Liability Company or Limited Partnership [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfSubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipTable" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_ScheduleOfSubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfSubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipTable" xlink:to="lab_us-gaap_ScheduleOfSubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipTable" xlink:type="arc" order="1"/>
    <link:label id="lab_ns_NumberofDaysWithinWhichDistributionIsPaidToCommonUnitholders_beb26330-3ae6-449a-822d-4184b1625477_terseLabel_en-US" xlink:label="lab_ns_NumberofDaysWithinWhichDistributionIsPaidToCommonUnitholders" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Number of days within which distribution is paid to common unitholders</link:label>
    <link:label id="lab_ns_NumberofDaysWithinWhichDistributionIsPaidToCommonUnitholders_label_en-US" xlink:label="lab_ns_NumberofDaysWithinWhichDistributionIsPaidToCommonUnitholders" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Number of Days Within Which Distribution Is Paid To Common Unitholders</link:label>
    <link:label id="lab_ns_NumberofDaysWithinWhichDistributionIsPaidToCommonUnitholders_documentation_en-US" xlink:label="lab_ns_NumberofDaysWithinWhichDistributionIsPaidToCommonUnitholders" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Number of days within which distribution must be paid to common unitholders after end of quarter (per the terms of the partnership agreement).</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ns_NumberofDaysWithinWhichDistributionIsPaidToCommonUnitholders" xlink:href="ns-20200930.xsd#ns_NumberofDaysWithinWhichDistributionIsPaidToCommonUnitholders"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ns_NumberofDaysWithinWhichDistributionIsPaidToCommonUnitholders" xlink:to="lab_ns_NumberofDaysWithinWhichDistributionIsPaidToCommonUnitholders" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LimitedPartnersCapitalAccountUnitsOutstanding_a2209dad-b26f-4457-bc99-431f7c065514_terseLabel_en-US" xlink:label="lab_us-gaap_LimitedPartnersCapitalAccountUnitsOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Limited partners common units outstanding</link:label>
    <link:label id="lab_us-gaap_LimitedPartnersCapitalAccountUnitsOutstanding_label_en-US" xlink:label="lab_us-gaap_LimitedPartnersCapitalAccountUnitsOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Limited Partners' Capital Account, Units Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LimitedPartnersCapitalAccountUnitsOutstanding" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_LimitedPartnersCapitalAccountUnitsOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LimitedPartnersCapitalAccountUnitsOutstanding" xlink:to="lab_us-gaap_LimitedPartnersCapitalAccountUnitsOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_3803f723-a1a7-4002-b209-6862bb1b81d7_totalLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net increase (decrease) in cash, cash equivalents and restricted cash</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_a3cedd4c-ae1d-4650-b021-47b5991c97c8_terseLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net increase (decrease) in cash, cash equivalents and restricted cash</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_label_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Cash, Cash Equivalents, Restricted Cash and Restricted Cash Equivalents, Period Increase (Decrease), Including Exchange Rate Effect</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect"/>
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    <link:label id="lab_us-gaap_PartnersCapitalNotesAbstract_bb6e1477-fa4f-4179-9236-b17e95885854_terseLabel_en-US" xlink:label="lab_us-gaap_PartnersCapitalNotesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Partners' Capital Notes [Abstract]</link:label>
    <link:label id="lab_us-gaap_PartnersCapitalNotesAbstract_label_en-US" xlink:label="lab_us-gaap_PartnersCapitalNotesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Partners' Capital Notes [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PartnersCapitalNotesAbstract" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_PartnersCapitalNotesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PartnersCapitalNotesAbstract" xlink:to="lab_us-gaap_PartnersCapitalNotesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HedgingRelationshipDomain_da2af8f7-4c6c-4ba5-baf8-6fd6f5be987d_terseLabel_en-US" xlink:label="lab_us-gaap_HedgingRelationshipDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Hedging Relationship [Domain]</link:label>
    <link:label id="lab_us-gaap_HedgingRelationshipDomain_label_en-US" xlink:label="lab_us-gaap_HedgingRelationshipDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Hedging Relationship [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HedgingRelationshipDomain" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_HedgingRelationshipDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HedgingRelationshipDomain" xlink:to="lab_us-gaap_HedgingRelationshipDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DistributionMadeToLimitedPartnerDistributionsDeclaredPerUnit_6952cb13-75b1-467f-a3e8-d5e3302ee324_verboseLabel_en-US" xlink:label="lab_us-gaap_DistributionMadeToLimitedPartnerDistributionsDeclaredPerUnit" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred unit distribution</link:label>
    <link:label id="lab_us-gaap_DistributionMadeToLimitedPartnerDistributionsDeclaredPerUnit_51a135dd-c203-4853-a75a-3a5757d47892_terseLabel_en-US" xlink:label="lab_us-gaap_DistributionMadeToLimitedPartnerDistributionsDeclaredPerUnit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Cash distributions per unit</link:label>
    <link:label id="lab_us-gaap_DistributionMadeToLimitedPartnerDistributionsDeclaredPerUnit_label_en-US" xlink:label="lab_us-gaap_DistributionMadeToLimitedPartnerDistributionsDeclaredPerUnit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Distribution Made to Limited Partner, Distributions Declared, Per Unit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DistributionMadeToLimitedPartnerDistributionsDeclaredPerUnit" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_DistributionMadeToLimitedPartnerDistributionsDeclaredPerUnit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DistributionMadeToLimitedPartnerDistributionsDeclaredPerUnit" xlink:to="lab_us-gaap_DistributionMadeToLimitedPartnerDistributionsDeclaredPerUnit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditFacilityInterestRateDescription_a103e379-a837-4b9e-92be-a7b001e85f1a_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityInterestRateDescription" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Line of credit facility, interest rate description</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityInterestRateDescription_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityInterestRateDescription" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Line of Credit Facility, Interest Rate Description</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityInterestRateDescription" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_LineOfCreditFacilityInterestRateDescription"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityInterestRateDescription" xlink:to="lab_us-gaap_LineOfCreditFacilityInterestRateDescription" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CostsAndExpensesAbstract_553f838a-a17c-4a4f-b994-9e7a64b1c9b5_terseLabel_en-US" xlink:label="lab_us-gaap_CostsAndExpensesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Costs and expenses:</link:label>
    <link:label id="lab_us-gaap_CostsAndExpensesAbstract_label_en-US" xlink:label="lab_us-gaap_CostsAndExpensesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Costs and Expenses [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CostsAndExpensesAbstract" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_CostsAndExpensesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CostsAndExpensesAbstract" xlink:to="lab_us-gaap_CostsAndExpensesAbstract" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_SubsequentEventsAbstract_label_en-US" xlink:label="lab_us-gaap_SubsequentEventsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Subsequent Events [Abstract]</link:label>
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    <link:label id="lab_us-gaap_CashAndCashEquivalentsMember_687bb2f4-fc45-4c5f-bb8e-ad099c562736_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Cash and cash equivalents [Member]</link:label>
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    <link:label id="lab_us-gaap_CashFlowHedgingMember_cff93a72-256e-47ef-bd98-9aa73e04e1dc_terseLabel_en-US" xlink:label="lab_us-gaap_CashFlowHedgingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Cash Flow Hedges</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashFlowHedgingMember" xlink:to="lab_us-gaap_CashFlowHedgingMember" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_InterestPaidNet_efdb154a-a849-4063-9406-46bc328d7b8b_terseLabel_en-US" xlink:label="lab_us-gaap_InterestPaidNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Cash paid for interest, net of amount capitalized</link:label>
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    <link:label id="lab_ns_GoZoneBondsDueAugust2041Member_d3c4fce2-1f9f-4485-90ae-854f94c824bf_terseLabel_en-US" xlink:label="lab_ns_GoZoneBondsDueAugust2041Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">GoZone Bonds Due August 2041</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Revenues" xlink:to="lab_us-gaap_Revenues" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementClassOfStockAxis_7452a140-12da-47e6-8d8e-ac5bde830fd8_terseLabel_en-US" xlink:label="lab_us-gaap_StatementClassOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Class of Stock [Axis]</link:label>
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    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_a375bc54-9d8f-4f10-a69f-f6f859785edb_periodStartLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Cash, cash equivalents and restricted cash as of the beginning of the period</link:label>
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    <link:label id="lab_us-gaap_AccruedLiabilitiesCurrent_label_en-US" xlink:label="lab_us-gaap_AccruedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accrued Liabilities, Current</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccruedLiabilitiesCurrent" xlink:to="lab_us-gaap_AccruedLiabilitiesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_ns_FuelsMarketingSegmentMember_09aa10bc-79c3-430c-a7d4-5e5385b2a30e_terseLabel_en-US" xlink:label="lab_ns_FuelsMarketingSegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fuels Marketing Segment</link:label>
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    <link:label id="lab_ns_FuelsMarketingSegmentMember_documentation_en-US" xlink:label="lab_ns_FuelsMarketingSegmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Segment of the business engaged in the marketing of products</link:label>
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    <link:label id="lab_dei_LocalPhoneNumber_c280dcc0-847a-4c85-b0c8-a4bc58ce5af9_terseLabel_en-US" xlink:label="lab_dei_LocalPhoneNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Local Phone Number</link:label>
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    <link:label id="lab_ns_NumberOfTerminals_be1cea2c-a3a9-432d-b1b2-3346641ee793_terseLabel_en-US" xlink:label="lab_ns_NumberOfTerminals" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Number of terminals</link:label>
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    <link:label id="lab_ns_NumberOfTerminals_documentation_en-US" xlink:label="lab_ns_NumberOfTerminals" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Number of Terminals</link:label>
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    <link:label id="lab_us-gaap_TemporaryEquitySharesOutstanding_c80bcc09-b2ea-4322-8509-7ef5a9f22efc_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquitySharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Series D preferred units outstanding</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfStockByClassTable_f52cf015-9518-4ffb-a4ae-6f494f8999d5_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfStockByClassTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Schedule of Stock by Class [Table]</link:label>
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    <link:label id="lab_ns_DisposalGroupIncludingDiscontinuedOperationTotalExpenses_documentation_en-US" xlink:label="lab_ns_DisposalGroupIncludingDiscontinuedOperationTotalExpenses" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Amount of total expenses attributable to disposal group, including, but not limited to, discontinued operation.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ns_DisposalGroupIncludingDiscontinuedOperationTotalExpenses" xlink:href="ns-20200930.xsd#ns_DisposalGroupIncludingDiscontinuedOperationTotalExpenses"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ns_DisposalGroupIncludingDiscontinuedOperationTotalExpenses" xlink:to="lab_ns_DisposalGroupIncludingDiscontinuedOperationTotalExpenses" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DiscontinuedOperationTaxEffectOfDiscontinuedOperation_acd095dc-c2df-42eb-8244-a3a75751027c_terseLabel_en-US" xlink:label="lab_us-gaap_DiscontinuedOperationTaxEffectOfDiscontinuedOperation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Income tax expense</link:label>
    <link:label id="lab_us-gaap_DiscontinuedOperationTaxEffectOfDiscontinuedOperation_label_en-US" xlink:label="lab_us-gaap_DiscontinuedOperationTaxEffectOfDiscontinuedOperation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Discontinued Operation, Tax Effect of Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DiscontinuedOperationTaxEffectOfDiscontinuedOperation" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_DiscontinuedOperationTaxEffectOfDiscontinuedOperation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DiscontinuedOperationTaxEffectOfDiscontinuedOperation" xlink:to="lab_us-gaap_DiscontinuedOperationTaxEffectOfDiscontinuedOperation" xlink:type="arc" order="1"/>
    <link:label id="lab_ns_SeriesCPreferredLimitedPartnerMember_01d650e5-3e3d-4bae-a6bf-ed9f9f9ebdcf_terseLabel_en-US" xlink:label="lab_ns_SeriesCPreferredLimitedPartnerMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Series C Preferred Limited Partner [Member]</link:label>
    <link:label id="lab_ns_SeriesCPreferredLimitedPartnerMember_label_en-US" xlink:label="lab_ns_SeriesCPreferredLimitedPartnerMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Series C Preferred Limited Partner [Member]</link:label>
    <link:label id="lab_ns_SeriesCPreferredLimitedPartnerMember_documentation_en-US" xlink:label="lab_ns_SeriesCPreferredLimitedPartnerMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Series C Preferred Limited Partner - Partner with preferential rights over the common limited partner in areas that could include, but are not limited to, liquidation, redemption, conversion, tax status of distribution or sharing in distributions.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ns_SeriesCPreferredLimitedPartnerMember" xlink:href="ns-20200930.xsd#ns_SeriesCPreferredLimitedPartnerMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ns_SeriesCPreferredLimitedPartnerMember" xlink:to="lab_ns_SeriesCPreferredLimitedPartnerMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ConsolidationEliminationsMember_a9824ce4-1402-4ef8-b396-a4d30d4f8c9f_terseLabel_en-US" xlink:label="lab_srt_ConsolidationEliminationsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Eliminations [Member]</link:label>
    <link:label id="lab_srt_ConsolidationEliminationsMember_label_en-US" xlink:label="lab_srt_ConsolidationEliminationsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Consolidation, Eliminations [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidationEliminationsMember" xlink:href="http://xbrl.fasb.org/srt/2020/elts/srt-2020-01-31.xsd#srt_ConsolidationEliminationsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ConsolidationEliminationsMember" xlink:to="lab_srt_ConsolidationEliminationsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentCarryingAmount_bd8e4194-9dfe-4a41-9686-05fdd549f47f_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Long-term debt</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentCarryingAmount_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Long-term Debt, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentCarryingAmount" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_DebtInstrumentCarryingAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentCarryingAmount" xlink:to="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_ns_CommonLimitedPartnerDistribution_041f6015-37bc-47a4-af12-55741f7d6683_negatedLabel_en-US" xlink:label="lab_ns_CommonLimitedPartnerDistribution" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Distributions to common limited partners</link:label>
    <link:label id="lab_ns_CommonLimitedPartnerDistribution_5855a80e-ba5a-4529-8afd-1d32c03fa026_verboseLabel_en-US" xlink:label="lab_ns_CommonLimitedPartnerDistribution" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Distributions to common limited partners</link:label>
    <link:label id="lab_ns_CommonLimitedPartnerDistribution_label_en-US" xlink:label="lab_ns_CommonLimitedPartnerDistribution" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Common Limited Partner Distribution</link:label>
    <link:label id="lab_ns_CommonLimitedPartnerDistribution_documentation_en-US" xlink:label="lab_ns_CommonLimitedPartnerDistribution" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Distribution amount earned during the period allocated to the common limited partners.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ns_CommonLimitedPartnerDistribution" xlink:href="ns-20200930.xsd#ns_CommonLimitedPartnerDistribution"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ns_CommonLimitedPartnerDistribution" xlink:to="lab_ns_CommonLimitedPartnerDistribution" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressAddressLine1_6ef62149-4e31-4b8d-a7e7-3bfa6827cb1a_terseLabel_en-US" xlink:label="lab_dei_EntityAddressAddressLine1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Address, Street</link:label>
    <link:label id="lab_dei_EntityAddressAddressLine1_label_en-US" xlink:label="lab_dei_EntityAddressAddressLine1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Address, Address Line One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressAddressLine1" xlink:href="https://xbrl.sec.gov/dei/2020/dei-2020-01-31.xsd#dei_EntityAddressAddressLine1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressAddressLine1" xlink:to="lab_dei_EntityAddressAddressLine1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromDivestitureOfBusinessesNetOfCashDivested_2469545b-2c21-42f8-a39d-2333312a44e5_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromDivestitureOfBusinessesNetOfCashDivested" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Proceeds from sale</link:label>
    <link:label id="lab_us-gaap_ProceedsFromDivestitureOfBusinessesNetOfCashDivested_label_en-US" xlink:label="lab_us-gaap_ProceedsFromDivestitureOfBusinessesNetOfCashDivested" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Proceeds from Divestiture of Businesses, Net of Cash Divested</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromDivestitureOfBusinessesNetOfCashDivested" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_ProceedsFromDivestitureOfBusinessesNetOfCashDivested"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromDivestitureOfBusinessesNetOfCashDivested" xlink:to="lab_us-gaap_ProceedsFromDivestitureOfBusinessesNetOfCashDivested" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ContractWithCustomerLiability_0a32fe3b-49ee-4e42-abe5-5139c01a2250_negatedLabel_en-US" xlink:label="lab_us-gaap_ContractWithCustomerLiability" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_ContractWithCustomerLiability_label_en-US" xlink:label="lab_us-gaap_ContractWithCustomerLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Contract with Customer, Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractWithCustomerLiability" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_ContractWithCustomerLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ContractWithCustomerLiability" xlink:to="lab_us-gaap_ContractWithCustomerLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets_df7fe1c8-cd33-45be-a8cf-6e10b4650b15_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Decrease (increase) in other currrent assets</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Increase (Decrease) in Other Operating Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_IncreaseDecreaseInOtherOperatingAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:to="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityEmergingGrowthCompany_b0fc66ba-b0cf-4c6d-b2ed-a9d49d99e965_terseLabel_en-US" xlink:label="lab_dei_EntityEmergingGrowthCompany" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Emerging Growth Company</link:label>
    <link:label id="lab_dei_EntityEmergingGrowthCompany_label_en-US" xlink:label="lab_dei_EntityEmergingGrowthCompany" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Emerging Growth Company</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityEmergingGrowthCompany" xlink:href="https://xbrl.sec.gov/dei/2020/dei-2020-01-31.xsd#dei_EntityEmergingGrowthCompany"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityEmergingGrowthCompany" xlink:to="lab_dei_EntityEmergingGrowthCompany" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionTable_fc6aede0-f39f-4212-8a29-54169862ea26_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Revenue, Remaining Performance Obligation, Expected Timing of Satisfaction [Table]</link:label>
    <link:label id="lab_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionTable_label_en-US" xlink:label="lab_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Revenue, Remaining Performance Obligation, Expected Timing of Satisfaction [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionTable" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionTable" xlink:to="lab_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnusualOrInfrequentItemTable_8877df04-ab8f-48c2-a954-7a3f2f5ae2fa_terseLabel_en-US" xlink:label="lab_us-gaap_UnusualOrInfrequentItemTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Unusual or Infrequent Item, or Both [Table]</link:label>
    <link:label id="lab_us-gaap_UnusualOrInfrequentItemTable_label_en-US" xlink:label="lab_us-gaap_UnusualOrInfrequentItemTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Unusual or Infrequent Item, or Both [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnusualOrInfrequentItemTable" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_UnusualOrInfrequentItemTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnusualOrInfrequentItemTable" xlink:to="lab_us-gaap_UnusualOrInfrequentItemTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeLiability_5b0bd2b6-057f-429c-803c-8c42b156f71f_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeLiability" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Liability derivatives</link:label>
    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeLiability_label_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative Liability, Fair Value, Gross Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeFairValueOfDerivativeLiability" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_DerivativeFairValueOfDerivativeLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeFairValueOfDerivativeLiability" xlink:to="lab_us-gaap_DerivativeFairValueOfDerivativeLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_0d3e4e8f-5207-4a3e-a56a-3b18b9f0d0c7_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Maximum borrowing capacity</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Line of Credit Facility, Maximum Borrowing Capacity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:to="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditFacilityCovenantTerms_f9fdee7c-5acf-4349-a63a-973ce90887dd_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityCovenantTerms" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Line of credit facility, covenant terms</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityCovenantTerms_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityCovenantTerms" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Line of Credit Facility, Covenant Terms</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityCovenantTerms" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_LineOfCreditFacilityCovenantTerms"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityCovenantTerms" xlink:to="lab_us-gaap_LineOfCreditFacilityCovenantTerms" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MaximumMember_e5acb234-2fe2-4bdb-85a0-7ff3a1c5facd_terseLabel_en-US" xlink:label="lab_srt_MaximumMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Maximum [Member]</link:label>
    <link:label id="lab_srt_MaximumMember_label_en-US" xlink:label="lab_srt_MaximumMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Maximum [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MaximumMember" xlink:href="http://xbrl.fasb.org/srt/2020/elts/srt-2020-01-31.xsd#srt_MaximumMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MaximumMember" xlink:to="lab_srt_MaximumMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DistributionsMadeToLimitedPartnerTable_45373e81-0631-4419-b099-f95e601fb717_terseLabel_en-US" xlink:label="lab_us-gaap_DistributionsMadeToLimitedPartnerTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Distributions Made to Preferred Limited Partner [Table]</link:label>
    <link:label id="lab_us-gaap_DistributionsMadeToLimitedPartnerTable_5ccb3452-6fdf-4060-a6b1-34aed823d646_verboseLabel_en-US" xlink:label="lab_us-gaap_DistributionsMadeToLimitedPartnerTable" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Distributions Made to Common Limited Partner [Table]</link:label>
    <link:label id="lab_us-gaap_DistributionsMadeToLimitedPartnerTable_label_en-US" xlink:label="lab_us-gaap_DistributionsMadeToLimitedPartnerTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Distributions Made to Limited Partner [Table]</link:label>
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    <link:label id="lab_us-gaap_BusinessInterruptionLossAxis_bd3800aa-76d6-433d-8554-74eac50d24dd_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessInterruptionLossAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Business Interruption Loss [Axis]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessInterruptionLossAxis" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_BusinessInterruptionLossAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessInterruptionLossAxis" xlink:to="lab_us-gaap_BusinessInterruptionLossAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities_f3f0cb88-c202-41a6-9e79-03f97927382a_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net cash (used in) provided by investing activities</link:label>
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    <link:label id="lab_dei_TradingSymbol_25077cb8-a5d2-498f-9f07-74140e10a646_terseLabel_en-US" xlink:label="lab_dei_TradingSymbol" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Trading Symbol</link:label>
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    <link:label id="lab_us-gaap_DividendsShareBasedCompensationCash_6f174ca6-323b-4437-89d7-bb877bfef0c4_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DividendsShareBasedCompensationCash" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Distribution equivalent rights to restricted units</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DividendsShareBasedCompensationCash" xlink:to="lab_us-gaap_DividendsShareBasedCompensationCash" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ScheduleOfCondensedBalanceSheetTableTextBlock_15f1c546-c90d-4f40-b0fb-01cc877d2e14_terseLabel_en-US" xlink:label="lab_srt_ScheduleOfCondensedBalanceSheetTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Condensed Balance Sheet</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_srt_ScheduleOfCondensedBalanceSheetTableTextBlock" xlink:href="http://xbrl.fasb.org/srt/2020/elts/srt-2020-01-31.xsd#srt_ScheduleOfCondensedBalanceSheetTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ScheduleOfCondensedBalanceSheetTableTextBlock" xlink:to="lab_srt_ScheduleOfCondensedBalanceSheetTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ns_SeriesDPreferredLimitedPartnerMember_218d7e46-4b3c-4b51-80c6-094d642681fc_terseLabel_en-US" xlink:label="lab_ns_SeriesDPreferredLimitedPartnerMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Series D Preferred Limited Partner [Member]</link:label>
    <link:label id="lab_ns_SeriesDPreferredLimitedPartnerMember_label_en-US" xlink:label="lab_ns_SeriesDPreferredLimitedPartnerMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Series D Preferred Limited Partner [Member]</link:label>
    <link:label id="lab_ns_SeriesDPreferredLimitedPartnerMember_documentation_en-US" xlink:label="lab_ns_SeriesDPreferredLimitedPartnerMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Series D Preferred Limited Partner - Partner with preferential rights over the common limited partner in areas that could include, but are not limited to; liquidation, redemption, conversion, tax status of distribution of sharing in distributions.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ns_SeriesDPreferredLimitedPartnerMember" xlink:href="ns-20200930.xsd#ns_SeriesDPreferredLimitedPartnerMember"/>
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    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable_e3986c80-9efd-42e4-89ed-bd5cf18e36e2_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss) [Table]</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss) [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable" xlink:to="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DiscontinuedOperationsAndDisposalGroupsAbstract_0c9ec3c2-4fd9-4d73-b826-91c7bb3edeb3_terseLabel_en-US" xlink:label="lab_us-gaap_DiscontinuedOperationsAndDisposalGroupsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Discontinued Operations and Disposal Groups [Abstract]</link:label>
    <link:label id="lab_us-gaap_DiscontinuedOperationsAndDisposalGroupsAbstract_label_en-US" xlink:label="lab_us-gaap_DiscontinuedOperationsAndDisposalGroupsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Discontinued Operations and Disposal Groups [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DiscontinuedOperationsAndDisposalGroupsAbstract" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_DiscontinuedOperationsAndDisposalGroupsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DiscontinuedOperationsAndDisposalGroupsAbstract" xlink:to="lab_us-gaap_DiscontinuedOperationsAndDisposalGroupsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ns_DisposalGroupIncludingDiscontinuedOperationCostOfRevenues_9c01dd14-28ac-4064-8015-88ab0053bbcc_terseLabel_en-US" xlink:label="lab_ns_DisposalGroupIncludingDiscontinuedOperationCostOfRevenues" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Cost of revenues</link:label>
    <link:label id="lab_ns_DisposalGroupIncludingDiscontinuedOperationCostOfRevenues_label_en-US" xlink:label="lab_ns_DisposalGroupIncludingDiscontinuedOperationCostOfRevenues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">DisposalGroupIncludingDiscontinuedOperationCostOfRevenues</link:label>
    <link:label id="lab_ns_DisposalGroupIncludingDiscontinuedOperationCostOfRevenues_documentation_en-US" xlink:label="lab_ns_DisposalGroupIncludingDiscontinuedOperationCostOfRevenues" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Amount of cost of revenues attributable to disposal group, including, but not limited to, discontinued operation.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ns_DisposalGroupIncludingDiscontinuedOperationCostOfRevenues" xlink:href="ns-20200930.xsd#ns_DisposalGroupIncludingDiscontinuedOperationCostOfRevenues"/>
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    <link:label id="lab_us-gaap_DebtInstrumentDescription_afcb6d2d-3d47-4f6f-94a3-1849d0d5705c_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentDescription" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Debt instrument, description</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentDescription_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentDescription" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Debt Instrument, Description</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentDescription" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_DebtInstrumentDescription"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentDescription" xlink:to="lab_us-gaap_DebtInstrumentDescription" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage_c485e83b-9841-41dd-81f9-8dc214c066b0_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Long-term debt, commitment fee, percent</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Line of Credit Facility, Unused Capacity, Commitment Fee Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage"/>
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    <link:label id="lab_ns_PreferredStockDistributionsPeriodPeriodDuringWhichRateIsEffectiveJune292023andthereafterMember_58ed41e6-70f4-4fe1-a171-d1230a009d74_terseLabel_en-US" xlink:label="lab_ns_PreferredStockDistributionsPeriodPeriodDuringWhichRateIsEffectiveJune292023andthereafterMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred Stock, Distributions, Period - June 29, 2023 and thereafter [Member]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ns_PreferredStockDistributionsPeriodPeriodDuringWhichRateIsEffectiveJune292023andthereafterMember" xlink:href="ns-20200930.xsd#ns_PreferredStockDistributionsPeriodPeriodDuringWhichRateIsEffectiveJune292023andthereafterMember"/>
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    <link:label id="lab_us-gaap_ContractWithCustomerAssetNet_a9479edc-8825-4bff-acf9-a4d87edcef9a_verboseLabel_en-US" xlink:label="lab_us-gaap_ContractWithCustomerAssetNet" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_ContractWithCustomerAssetNet_label_en-US" xlink:label="lab_us-gaap_ContractWithCustomerAssetNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Contract with Customer, Asset, after Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractWithCustomerAssetNet" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_ContractWithCustomerAssetNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ContractWithCustomerAssetNet" xlink:to="lab_us-gaap_ContractWithCustomerAssetNet" xlink:type="arc" order="1"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionTableTextBlock" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionTableTextBlock" xlink:to="lab_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionTableTextBlock" xlink:type="arc" order="1"/>
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