Abstract-We address the joint channel assignment and power allocation question in a multichannel wireless (access point) network where channel states differ across channels as well as users, and vary with time. Our goal is to obtain channel assignment and power allocation solutions that can dynamically adapt to changing channel conditions, and would maximize system throughput under per-user bandwidth (QoS) constraints, in a long-term sense. Using stochastic optimization techniques, we obtain an optimal scheduling policy that operates without knowledge of arrival rates and channel statistics (depending only on the instantaneous channel states and the queue lengths), and attains the overall system throughput that is arbitrarily close to the maximum achievable value with all per-user bandwidth constraints satisfied.