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Note 7 - Income Taxes - Summary of Valuation Allowance (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2022	Dec. 31, 2021
Valuation allowance at beginning of period	$ 18,823	$ 13,867
Income tax benefit	6,873	4,956
Release of valuation allowance	0	0
Valuation allowance at end of period	$ 25,696	$ 18,823

X

- Definition

Represents valuation allowance releases for deferred tax assets.

+ References

No definition available.

+ Details

Name:	mbrx_DeferredTaxAssetsValuationAllowanceReleases
Namespace Prefix:	mbrx_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

X

- Definition

Amount of deferred tax assets for which it is more likely than not that a tax benefit will not be realized.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (c)
-URI https://asc.fasb.org/extlink&oid=121826272&loc=d3e32537-109319

+ Details

Name:	us-gaap_DeferredTaxAssetsValuationAllowance
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

X

- Definition

Amount of increase (decrease) in the valuation allowance for a specified deferred tax asset.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 50
-Paragraph 2
-URI https://asc.fasb.org/extlink&oid=121826272&loc=d3e32537-109319

+ Details

Name:	us-gaap_ValuationAllowanceDeferredTaxAssetChangeInAmount
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration