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Revenues
 6 Months Ended
Jun. 30, 2024
Revenue from Contract with Customer [Abstract]  
Revenues Revenues
For the three months ended June 30, 2024 and 2023, we recognized revenues of $371.7 million and $346.8 million, respectively. Of the $371.7 million recognized in the second quarter of 2024, we recognized revenues of $18.2 million from obligations satisfied, or partially satisfied, in prior periods, of which $13.2 million was due to changes in the estimates of our variable consideration under performance-based billing arrangements and $5.0 million was due to the release of allowances on receivables from clients and unbilled services. Of the $346.8 million recognized in the second quarter of 2023, we recognized revenues of $14.8 million from obligations satisfied, or partially satisfied, in prior periods, of which $12.6 million was due to changes in the estimates of our variable consideration under performance-based billing arrangements and $2.2 million was due to the release of allowances on receivables from clients and unbilled services.
For the six months ended June 30, 2024 and 2023, we recognized revenues of $727.6 million and $664.7 million, respectively. Of the $727.6 million recognized in the first six months of 2024, we recognized revenues of $20.5 million from obligations satisfied, or partially satisfied, in prior periods, of which $17.2 million was due to changes in the estimates of our variable consideration under performance-based billing arrangements and $3.3 million was due to the release of allowances on receivables from clients and unbilled services. Of the $664.7 million recognized in the first six months of 2023, we recognized revenues of $6.3 million from obligations satisfied, or partially satisfied, in prior periods, of which $5.0 million was due to changes in the estimates of our variable consideration under performance-based billing arrangements and $1.3 million was due to the release of allowances on receivables from clients and unbilled services.
As of June 30, 2024, we had $216.5 million of remaining performance obligations under engagements with original expected durations greater than one year. These remaining performance obligations exclude variable consideration which has been excluded from the total transaction price due to the constraint and performance obligations under time-and-expense engagements which are recognized in the amount invoiced. Of the $216.5 million of performance obligations, we expect to recognize $46.9 million as revenue in 2024, $65.7 million in 2025, and the remaining $103.9 million thereafter. Actual revenue recognition could differ from these amounts as a result of changes in the estimated timing of work to be performed, adjustments to estimated variable consideration in performance-based arrangements, or other factors.
Contract Assets and Liabilities
The payment terms and conditions in our customer contracts vary. Differences between the timing of billings and the recognition of revenue are recognized as either unbilled services or deferred revenues in the consolidated balance sheets.
Unbilled services include revenues recognized for services performed but not yet billed to clients. Services performed that we are not yet entitled to bill because certain events, such as the completion of the measurement period or client approval in performance-based engagements, must occur are recorded as contract assets and included within unbilled services, net. The contract asset, net balance as of June 30, 2024 and December 31, 2023 was $75.7 million and $70.1 million, respectively. The $5.6 million million increase primarily reflects timing differences between the completion of our performance obligations and the amounts billed or billable to clients in accordance with their contractual billing terms.
Client prepayments and retainers are classified as deferred revenues and recognized over future periods in accordance with the applicable engagement agreement and our revenue recognition accounting policy. Our deferred revenues balance as of June 30, 2024 and
December 31, 2023 was $28.6 million and $22.5 million, respectively. The $6.1 million increase reflects timing differences between client payments in accordance with their contract terms and the completion of our performance obligations. For the three and six months ended June 30, 2024, $4.2 million and $19.6 million of revenues recognized were included in the deferred revenue balance as of December 31, 2023, respectively.