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The paper deals with the problem of blind mitigation of intersymbol interference (ISI) as well as multiple-access interference (MAI) in asynchronous high data-rate direct-sequence code-division multiple-access systems. A blind adaptive multiuser receiver based on the constant-modulus algorithm (CMA) is proposed, which demodulates each desired user by exploiting only the knowledge of its spreading code, without requiring estimation of the users's channels and timings. In order to overcome the CMA interference capture problem, which arises in a multiuser scenario, a two-stage adaptive receiver is adopted: In the first stage, partial MAI and ISI suppression is blindly achieved by exploiting the desired user signature structure properties; in the second stage, the residual MAI and the ISI are removed by using the CMA, and the information symbols of the desired user are reliably recovered. Theoretical analysis and simulation results show that the first stage is an effective blind adaptive strategy which allows the CMA detector in the second stage to lock on the desired-user symbol, at a particular delay. The proposed blind receiver achieves a significant performance gain in comparison with existing blind methods.