A new adaptive resource allocation scheme is proposed in orthogonal frequency-division multiple access (OFDMA) systems with rate proportionality constraints. The problem of maximizing the overall system capacity with constraints on bit-error rate, total transmission power and rate-proportionality for user requiring different classes of service is formulated. Since the optimal solution to the constrained fairness problem is extremely complex to obtain, a low-complexity suboptimal algorithm that separates subchannel allocation and power allocation is proposed. Firstly, the number of subchannels to be assigned to each user is determined based on the users' average signal-to-noise ratio and rate-proportion. Subchannels are subsequently distributed according to the modified max-min criterion. Lastly, iterative rateproportionality tracking algorithm is proposed for maximizing the capacity together with maintaining the rate proportionality constraint. Simulation results demonstrate that the proposed method can distribute the capacity more efficiently and fairly among users than other existing method.