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Direct-sequence code-division multiple access (CDMA) is considered for multiuser communication network in underwater acoustic channel, where extended multipath and rapid time-variability are encountered. To track and compensate the channel distortion, a decentralized hypothesis-feedback equalization (HFE) algorithm based on chip-rate update has been used[1]. But due to multiple access interference (MAI), its performance suffers degradation. For this reason, successive interference cancellation hypothesis-feedback equalization (SIC-HFE) algorithm is proposed, which combines the capabilities of HFE to track the time-varying channel and SIC implemented by cross-over feedback filters to cancel out the MAI effects between users. Simulation and experiment results show that the proposed algorithm can significantly improve the performance of asynchronous multiuser CDMA underwater communication system.