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In this paper, the utility-based resource allocation algorithms for the secondary users (SU) supporting heterogeneous services in orthogonal frequency division multiplexing (OFDM)-based cognitive radio cellular networks (CogCells) are studied. Two kinds of users are considered: best-effort-only service users and multiple services users. According to the convex optimization theory, the Lagrangian dual method is proposed, in which the joint subcarrier assignment and power allocation are performed to achieve the optimal solution. To simplify the computation complexity, a low complexity dynamic subcarrier allocation algorithm, named Max Utility for Multiple Services on Cognitive Radio (CR-MUMS), is formulated to extend the non-linear integer optimization to a continuous convex optimization. Final simulation results illustrate that the proposed algorithm with low computational complexity provides better optimal performance than Modified Largest Weighted Delay First (M-LWDF) and Proportional Fair (PF) algorithms.