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To provide differentiated service is one of important issues in the design of wireless ad hoc networks. Traditionally, the provisioning of the differentiated service to different types of traffic streams is mainly supported at the medium access control layer with strict priority scheduling or weighted priority scheduling. In this paper, we propose a novel solution, named as Power-Controlled Rate-Adaptive medium access control (PCRA-MAC) scheme, to provide differentiated service by cross-layer consideration and design. The PCRA-MAC scheme exploits the features of multi-rate and power adjustable wireless transceiver system to achieve different transmission rates to support differentiated service. To the best of our knowledge, the PCRA-MAC scheme is the first and the only MAC scheme that generates different transmission rates for different types of traffic by tuning transmission power. Simulation experiments have proved that the PCRA-MAC scheme can effectively supports differentiated service in the wireless ad hoc networks.