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IEEE 802.16 WiMAX (Worldwide Interoperability for Microwave Access) is a major standard technology for wireless metropolitan area networks. Quality-of-service (QoS) scheduling classes and mobility management are two main issues for supporting seamless high-speed communications. Previous works on WiMAX handoff however have mainly addressed a particular scenario or a specific QoS class. This work proposes a context-sensitive handoff scheme that supports the five IEEE 802.16 QoS scheduling classes.Furthermore, it is energy-aware - it may switch to energy-saving mode during a handoff. Performance evaluation shows that,comparing with three existing methods, the proposed scheme successfully supports the five QoS classes in both layers 2 and 3 handoff, reduces end-to-end handoff delay, delay jitter, and service disruption time. It also increases throughput and energy efficiency.We believe that this work is a significant contribution on providing high-quality, seamless data and media streaming over IEEE802.16 networks.