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The combination of cellular networks with wireless ad-hoc networks composed of cognitive radio (CR) enabled terminals can not only address the inherent capacity and coverage limitations, but also increase the spectrum utilization as a result of opportunistic spectrum usage characterized by cognitive radio. In this paper, the network environment is referred to as CR-MANET, including location management, network handoff, spectrum handoff where the traditional concept of mobility management is largely extended. After several anticipatory challenges facing the CR-MANET being brought forward in this paper, an appropriate model for cooperative and cross-layer design is proposed. Finally, the main open research issues for efficient spectrum handoff and network mobility management are analyzed detail, which include spectrum handoff and performance optimization, location areas management, location update and paging, network handoff and QoS guarantee.