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Like many wireless systems, Orthogonal Frequency Division Multiplexing (OFDM) needs proper allocation of limited resources such as total transmit power and available frequency bandwidth among the users to meet their service requirements. In this paper, different versions of two evolutionary approaches, Differential Evolution (DE) and Particle Swarm Optimization (PSO) have been applied for adaptive sub-carrier and bit allocations to minimize the overall transmit power of a multiuser OFDM system. Each user will be assigned a number of sub-carriers with at least one minimum sub-carrier even at the worst case. Then the number of bits and the transmit power level for each user are calculated to obtain the optimum requirements. Simulation results show that both the approaches outperform the conventional static and many other dynamic resource allocation schemes in multi-user scenario. The results also reveal that the employed two different schemes of DE show better performances than the original and modified versions of PSO.