A multiuser detection strategy for coherent demodulation in an asynchronous code-division multiple-access system is proposed and analyzed. The resulting detectors process the sufficient statistics via a multistage algorithm. This algorithm is based on a successive multiple-access interference annihilation scheme. An efficient real-time implementation of the multistage algorithm with a fixed decoding delay is obtained and it is shown to require a computational complexity/symbol which is linear in the number of users A'. Hence, the multistage detector contrasts the optimum demodulator, which is based on a dynamic programming algorithm; has a variable decoding delay; and a software complexity per symbol that is exponential in K [18]. Further, an exact expression for the probability of error is obtained for the two-stage detector. The probability of error computations show that the two-stage receiver is particularly well suited for “near-far” situations. In fact, performance approaches that of single-user communications as the interfering signals become stronger. The near-far problem is therefore alleviated. Further, significant performance gains over the conventional receiver are obtained even for relatively high bandwidth efficiency situations. © 1990 IEEE