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The quality of service (QoS) performance of wireless multiple access to an asynchronous transfer mode (ATM) network is investigated. Multiple access is implemented using a polling strategy with nonpreemptive priority to handle constant bit rate (CBR), variable bit rate (VBR) and available bit rate (ABR) services. Sufficient conditions are derived for all CBR sources to satisfy their jitter constraints and all VBR sources to their delay constraints. Under these conditions, tight analytical bounds are derived.