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In OFDMA-based Cognitive Radio (CR) systems, how to deal with the time-varying nature of available spectrum resources has become a hotspot and challenging problem in resource allocation. Traditional resource allocation algorithm can not guarantee proportional rates among non-real-time CR user (CRU) because the number of available subchannels is smaller than the number of CRUs in some OFDM symbol durations. In this paper, taking the maximizing of the sum-rate of all CRUs as the optimization objective, we propose a resource allocation algorithm in OFDMA-based CR systems using dual methods which can maintain statistical proportional rates among CRUs while keeping the interference introduced to Primary users (PU) under the specified thresholds. In contrast to traditional resource allocation algorithms, the proposed algorithm can achieve higher transmission rate and guarantee non-real-time services of CRUs.