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Source and channel coding over multiuser channels in which receivers have access to correlated source side information are considered. For several multiuser channel models necessary and sufficient conditions for optimal separation of the source and channel codes are obtained. In particular, the multiple-access channel, the compound multiple-access channel, the interference channel, and the two-way channel with correlated sources and correlated receiver side information are considered, and the optimality of separation is shown to hold for certain source and side information structures. Interestingly, the optimal separate source and channel codes identified for these models are not necessarily the optimal codes for the underlying source coding or the channel coding problems. In other words, while separation of the source and channel codes is optimal, the nature of these optimal codes is impacted by the joint design criterion.