Two promising classes of techniques are developed for e cient m ultiuser detection in codedivision multiple-access CDMA communication systems subject to fading due to time-varying multipath propagation. Both are designed to jointly suppress both intersymbol and multipleaccess interference inherent in such systems, and exploit all available time and frequency diversity.The rst is a family of linear receivers for time-varying multiuser channels that generalize familiar linear equalizers designed for traditional single-user linear time-invariant c hannels. Minimum mean-square error, zero-forcing, and matched-lter versions of such m ultiuser detectors are all developed within a common state-space framework, and have convenient recursive implementations. Performance issues as well as natural decision-feedback v ariants of the detector structure are both discussed.The second is a family of nonlinear receivers that are speci cally designed for use with spread-signature CDMA systems on time-varying multipath channels. These multiuser detectors employ a batch-iterative m ultipass decoding algorithm based on a successive-cancellation strategy. Several aspects of the performance of this algorithm are developed, including its monotonic convergence property.Collectively, these two classes of algorithmic structures for joint equalization, interference suppression, demodulation, and detection are representative of several emerging and interrelated approaches to receiver design for next-generation CDMA systems.