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In order to utilize the spectrum efficiently, the FCC announced Cognitive Radio (CR) technology as a candidate to implement negotiated or opportunistic spectrum sharing. It has received a great attention due to the ability to improve the spectrum utilization. In such a CR network, power control can increase the efficiency by adjusting the transmission power of the secondary users (SU). In this paper, we propose an adaptive distributed power control scheme for CR networks where the conventional power control schemes used in cellular system are modified to be used in cognitive radio network to consider the QoS requirements of both the Primary User (PU) and the SU simultaneously. Since the transmission power of each SU is constrained so that the interference temperature at the primary receiver caused by all SUs does not exceed the interference tolerance of the PU. As a result, the QoS requirement for the PU is always guaranteed.