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We consider the problem of allocating resources at a base station to many competing flows, when each flow is intended for a different receiver. The channel conditions may be time-varying and different for different receivers. It has been shown in A. Eryilmaz and R. Srikant (2005) that in a delay-free network, a combination of queue-length-based scheduling at the base station and congestion control at the end users can guarantee queue-length stability and fair resource allocation. In this paper, we extend this result to wireless networks where the congestion information from the base station is received with a feedback delay at the transmitters. The delays can be heterogeneous (i.e., different users may have different round-trip delays) and time-varying, but are assumed to be upper-bounded, with possibly very large upper bounds. We show that the joint congestion control-scheduling algorithm continues to be stable and continues to provide a fair allocation of the network resources.