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In this paper we consider the problem of radio resource (subcarriers and transmit power) management for QoS (quality of service: bit rate, bit error rate) support in cellular OFDMA systems with a fixed modulation. The major impairments considered are co-channel interference (CCI) and frequency selective fading. We propose an algorithm to distribute radio resources among multiple users according to their individual QoS traffic requirements, while at the same time maintaining the QoS of already established links in the co-channel cells. Due to minimization of transmit power and application of a dynamic channel assignment (DCA) approach, the radio resources are used more efficiently. Moreover, the considered resource allocation algorithm can be easily fit into the general contract-based QoS/CoS (cost of service) framework [S. Pietrzyk and G.J.M. Janssen, September 2002], which allows for flexible management of resources on the system level. Simulation results show a superior performance of the proposed method when compared to classical radio resource management techniques.