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With the increasing popularity of cognitive radio networks (CRNs), providing data transmissions with quality of service (QoS) requirements in such networks becomes one of the most important topics. In this paper we study QoS provisioning in an ad hoc CRN with spectrum underlay. Both streaming traffic and non-real-time (nrt) data traffic are considered. The former requires a low session outage probability and the latter requires a minimum average throughput. A joint connection admission and packet scheduling scheme is proposed in this paper. The connection admission control scheme limits the amount of traffic admitted into the system so that all admitted connections can receive their required QoS through the proposed packet scheduling schemes. Two packet transmission scheduling schemes are designed, one is optimum and assumes that a central controller can collect the global channel and interference conditions within the CRN and between the primary network and the CRN, while the other one is a heuristic scheme based on the link and interference conditions measured by the nodes in the CRN. In addition to achieving the required QoS, the scheduling schemes utilize the available radio resources fairly and efficiently. Numerical results demonstrate that when the traffic load at the primary network is relatively stationary, the proposed scheduling scheme can achieve very low and fair outage probability for all admitted streaming connections, and all admitted non-real-time data connections can receive the required throughput and fair delay performance.