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In this paper, we address the problem of medium-access control (MAC) in multihop networks. We focus on the first-come, first-serve (FCFS) collision-resolution algorithm, and for the two-destination case illustrate the difficulties that arise because of the interference between two populations of nodes that share a common channel. Specifically, a deadlock can arise when a commonly used improvement to the FCFS algorithm for the single-destination case is used. To eliminate this deadlock, we use a "group TDMA" mechanism, which separates the interfering groups, while permitting use of the best version of the FCFS algorithm. We demonstrate that use of group TDMA in conjunction with the FCFS algorithm can provide increased throughput and energy efficiency. Additionally, we extend our model to a cellular-like multihop network.