Motivated by the high complexity of the optimal sequence estimator for convolutionally coded asynchronous code-division multiple-access (CDMA) systems, developed by Giallorenzi and Wilson (see ibid., vol.44, no.8, p.997, 1996), and the potentially poor performance of the conventional receiver due to multiuser interference and the near-far problem, we examine relatively simple multiuser receivers which perform nearly as well as the optimal receiver. The multiuser receivers discussed are of two types. The first set of approaches are partitioned approaches that treat the multiuser interference equalization problem and the decoding problem separately. The second set of approaches are integrated approaches that perform both the equalization and decoding operations together. We study linear, decision feedback, and trellis/tree-based approaches in each category. The asymptotic efficiency of this receiver relative to an uncoded coherent binary phase shift keying (BPSK) receiver (termed asymptotic multiuser coding gain, or AMCG) is used as a performance criterion throughout. Also, computer simulations are used whenever the computation of the AMCG is not feasible. It is shown that a number of the approaches which are introduced achieve a high performance level with a moderate complexity.