Multiple-access interference (MAI) suppression techniques in DS/CDMA systems usually assume additive Gaussian noise. Minimum mean squared error (MMSE) detectors are near-far resistant in additive Gaussian noise channels. But the additive channel noise in many communication channels is often non-Gaussian and impulsive. Signal detection in non-Gaussian impulsive noise is traditionally focused on single-user channels. Symmetric alpha-stable (S[alpha] S) probability density functions can accurately model large classes of impulsive noise. The MMSE performance criterion cannot be used for S[alpha] S processes with 0<[alpha]<2 since they have infinite variance. This dissertation considers the problems of MAI suppression for DS/CDMA systems in the presence of additive non-Gaussian impulsive channel noise modeled as a S[alpha] S process with 1<[alpha]<2. These MAI suppression techniques help combat the near-far problem. First, the minimum dispersion (MD) criterion is introduced to suppress MAI. Linear MD detection can be viewed as expansion of the concept of the MMSE detection for Gaussian multiple-access channels to S[alpha] S non-Gaussian impulsive multiple-access channels. The linear MD detector is implemented adaptively using least mean p-norm (LMP) algorithm. The performance of the linear MD detector is analyzed in the context of a S[alpha] S process. Simulation results indicate that the adaptive MD detector shows good near-far resistance. Next, this dissertation presents a MRI suppression method using the least Lp-norm criterion. The iteratively reweighted least squares (IRLS) algorithm recursively approximates the least Lp-norm solution from weighted normal equations. Simulation results show that the proposed detector provides remarkable performance improvements over the adaptive MD detector in a wide range of near-far situations. The proposed detector has much better near-far resistance than the adaptive MD detector. Finally, fuzzy hybrid detector combines the adaptive MD detector and the hard-limiting matched filter (HLMF) detector. The HLMF detector performs well when the additive impulsive noise significantly dominates over MAI. Simulation results indicate significant performance improvements over the adaptive MD detector alone in impulsive noise-limited environments. When MAI dominates, the fuzzy hybrid detector nearly has the same performance as the adaptive MD detector.