The DQRUMA (distributed-queueing request update multiple access) protocol has been considered as an access protocol for the BAHAMA (broadband ad hoc wireless ATM local area network). However, it cannot support the service discipline of integrated multimedia traffic since it does not include any priority and access control policy. In this paper, we propose a nonpreemptive priority-based access control scheme for the DQRUMA protocol. Under such a scheme, modifying the CSMA/CA protocol in the contention period supports many levels of priorities such that user mobility (handoff) can be supported in BAHAMA. Besides, the proposed transmit-permission policy and adaptive bandwidth allocation scheme provide various QoS (quality-of-service) guarantees while maintaining high bandwidth utilization. Simulations show that it provides a good performance in ad hoc wireless ATM LAN environments.