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In this paper, we propose an algorithm for dynamic resource allocation in OFDM (orthogonal frequency division multiplexing) or OFDMA (OFD multiple access) based networks. We consider two groups of users consisting of group 1 called constant bit-rate (CBR) users (who are delay-sensitive and data-rate sensitive) and group 2 called best effort (BE) users. The proposed algorithm gives higher priority to the first group at the time of resource (transmitted power levels and subchannels) allocation to each user, to meet their CBR requirements. The performance of the proposed algorithm is evaluated through computer simulations, which show that the algorithm performs near optimum with the added superiority of meeting the bit requirements of the first group users.