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In this paper, we examine the performance of the iterative minimum mean-squared error (MMSE) adaptive receiver structure over asynchronous direct-sequence code-division multiple-access (DS-CDMA) channels. The receiver base-station uses estimates of the detected users' symbols to improve the convergence rate of the adaptive algorithm. The iterative algorithm used is based on the parallel interference cancellation (PIC) algorithm, and we examine the transient behaviour of both the least-mean-square (LMS) and the recursive-least squares (RLS) algorithms in asynchronous (i.e., reverse-link) DS-CDMA systems. Our results demonstrate a significant convergence improvement for the asynchronous case. It is shown that for the more severe asynchronous case, the convergence speed of the iterative algorithm is even better than the one achieved for the synchronous channel model. Also, for systems with no power control, the iterative algorithm is shown to be near-far resistance.