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The explosive growth in the use of real-time applications on mobile devices has resulted in new challenges to the design of routing protocols for cognitive radio ad hoc networks (CRANs). In this paper, we propose a new on-demand Quality-of-Service (QoS) routing, namely an energy efficient QoS routing (EQR) protocol for CRANs using TDMA. It can establish QoS routes with reserved bandwidth on a per flow basis in a multi-hop networks. The objective of this work is to establish bandwidth guaranteed QoS routes in small CRANs whose topologies change at low to medium rate. The protocol is based on DSR, and builds QoS routes only as needed. We assume the application is session-oriented and requires constant bandwidth. A session specifies its QoS requirement as the number of transmission timeslots it needs on its route from a source to a destination. For each session (flow), the QoS routing protocol will find both the route and the channel and timeslots for each link on the route. The simulation results show the effectiveness of our proposed approach with good generalization ability.