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Effective capacity, which provides the maximum constant arrival rate that a given service process can support while satisfying statistical queueing constraints, is analyzed in a multiuser scenario. In particular, the effective capacity region of fading multiple-access channels in the presence of quality of service (QoS) constraints is studied. Perfect channel side information is assumed to be available at both the transmitters and the receiver. It is initially assumed that the transmitters send the information at a fixed power level and, hence, do not employ power control policies. Under this assumption, the performance achieved by superposition coding with successive decoding techniques is investigated. It is shown that varying the decoding order with respect to the channel states can significantly increase the achievable throughput region. In the two-user case, the optimal decoding strategy is determined for the scenario in which the users have the same QoS constraints. The performance of orthogonal transmission strategies is also analyzed. It is shown that for certain QoS constraints, time-division multiple access can achieve better performance than superposition coding if fixed successive decoding order is used at the receiver side. In the subsequent analysis, power control policies are incorporated into the transmission strategies. The optimal power allocation policies for any fixed decoding order over all channel states are identified. For a given variable decoding-order strategy, the conditions that the optimal power control policies must satisfy are determined, and an algorithm that can be used to compute these optimal policies is provided.