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Full-duplex (FD) wireless is an attractive communication paradigm with high potential for improving network capacity and reducing delay in wireless networks. Despite significant progress on the physical layer development, the challenges associated with developing medium access control (MAC) protocols for heterogeneous networks composed of both legacy half-duplex (HD) and emerging FD devices have not been fully addressed. Therefore, we focus on the design and performance evaluation of scheduling algorithms for infrastructure-based heterogeneous HD-FD networks (composed of HD and FD users). We first show that centralized GreedyMaximal Scheduling (GMS) is throughput-optimal in heterogeneous HD-FD networks. We propose the Hybrid-GMS (H-GMS) algorithm, a distributed implementation of GMS that combines GMS and a queue-based random-access mechanism. We prove that H-GMS is throughputoptimal. Moreover, we analyze the delay performance of H-GMS by deriving lower bounds on the average queue length. We further demonstrate the benefits of upgrading HD nodes to FD nodes in terms of throughput gains for individual nodes and the whole network. Finally, we evaluate the performance of HGMS and its variants in terms of throughput, delay, and fairness between FD and HD users via extensive simulations. We show that in heterogeneous HD-FD networks, H-GMS achieves 16–30× better delay performance and improves fairness between HD and FD users by up to 50% compared with the fully decentralized Q-CSMA algorithm.