—The full-complexity soft-input/soft-output (SISO) multiuser detector based on the a posteriori probability (APP) algorithm has a computational complexity growing exponentially with the number of users. In this paper, we consider the multiuser detection problem from a combinatorial optimization viewpoint and develop a novel class of SISO multiuser detectors based on local search (LS) heuristics. By restricting the search to a small subset of the solution space and producing the APP based on a candidate list of potential solutions, the proposed detector can achieve bit-error-rate (BER) performance close to that of the APP algorithm with a significantly lower computational complexity. Keywords—Coded CDMA, list decoding, local search, multiuser detection, soft-input/soft-output