An iterative receiver structure is proposed for decoding multiuser information data in a turbo-coded DS-CDMA system. The receiver performs two successive soft-output decisions, achieved by a soft-input soft-output (SISO) multiuser detector and a bank of single-user SISO channel decoders, through an iterative process. At each iteration, extrinsic information is extracted from detection and decoding stages and is then used as a priori information in the next iteration, just as in turbo decoding. A low-complexity SISO multiuser detector is developed based on a novel nonlinear interference suppression technique, which makes use of both soft-interference cancellation and instantaneous linear MMSE filtering. Turbo multiuser detectors for both the simple synchronous CDMA channels and the more complex asynchronous multipath CDMA channels are developed.