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In order to reduce the complexity of the optimum ML multiuser sequence detector, which grows exponentially with the number of users, we propose suboptimum MLSE algorithms to detect DS/CDMA signals where the likelihood computations are based on reduced-state trellises. Thus, the number of complex arithmetic computations per detected symbol can be significantly reduced. We propose the use of single or multiple trellises. In both cases, tentative decisions based on the surviving paths are used to approximate the desired likelihood function. Simulation results show that the algorithm proposed can achieve significant complexity reduction with marginal performance degradation.