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Adaptive resource allocation is one of the most challenging tasks for multiuser orthogonal frequency division multiplexing (OFDM) systems. In this paper, two evolutionary approaches, genetic algorithm (GA) and particle swarm optimization (PSO) have been applied for adaptive subcarrier and bit allocations to minimize the overall transmit power of a multiuser OFDM system. Each user will be assigned a number of subcarriers with at least one minimum subcarrier even at the worst case. Then the number of bits and the transmit power level for each subcarrier are calculated. Simulation results show that both the evolutionary approaches outperform the conventional static resource allocation schemes considerably in multiuser scenario. The results further reveal that both the algorithms can handle large allocation of subcarriers without significant performance degradation. However the performance of PSO is found to be better than the GA in terms of execution time, simplicity and convergence.