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Underlay spectrum sharing in cognitive radio (CR) networks allows that the secondary user (SU) coexists with the primary user (PU) via primary spectrum sharing to the extent not to deteriorate the primary communication. It provides the SU with more access opportunity than the overlay one, but involves the risk that the quality of service (QoS) of the PU is degraded. In this context, controlling the transmit power of the SU can contribute to guarantee the QoS requirement of the PU and satisfy the QoS requirement for the SU's opportunistic communication to be reliable. However, finding an optimal set which maximizes the number of SUs satisfying both QoS requirements of the SU and the PU is a NP-complete problem. In this paper, we propose a joint power and admission control (JPAC) algorithm for CR networks which achieves a near-optimal performance without exhaustive search. The admission control algorithm removing SUs one-by-one is carried out jointly with the power control algorithm recursively until all remaining SUs satisfy the QoS requirements of the PU and the SU simultaneously. Through the simulation results, we demonstrate that the proposed JPAC algorithm guarantees the QoS requirement of the PU and adjoins the optimal performance with only reasonable force.