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The problem of broadcast channel access in single-hop and multihop ad hoc networks is considered. Two novel randomized and distributed channel access algorithms are developed and analyzed for single-hop and multihop networks, respectively. These algorithms are designed based on maximizing the worst-case channel efficiency, by optimizing some key parameters, including the backoff probability distribution and slot length. The proposed algorithm for single-hop networks offers significantly higher throughput than the CSMA methods when the traffic load is heavy, while still achieving good performance when the load is light or medium. The proposed algorithm for multihop networks can flexibly adapt to the traffic load, and offers much better throughput performance than the existing broadcast scheduling algorithms in light or medium load.