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The problem of how to optimally allocate available resources (e.g., bandwidth and power) in OFDM-based multicast wireless systems is important. Taking the maximization of system throughput as the design objective, an efficient resource allocation scheme is proposed for such systems under constraints on total system bandwidth and transmit power at the base station. Different from existing methods in the literature, our solution also considers the issue of fair resource utilization among multicast groups by guaranteeing minimum numbers of subchannels to be assigned to individual groups according to their respective channel conditions and group sizes. Once the subcarrier allocation is accomplished, the power allocation is performed in a water-filling fashion. The proposed algorithm distributes the throughput more flexibly and fairly between groups and, at the same time, still achieves a high total sum rate. The potential of our approach is confirmed by numerical results.