We propose adaptive modulation for maximum data rate in OFDMA systems with two types of users. The optimal subcarrier and bit allocation problems are formulated as nonlinear optimizations and converted into linear optimizations which are solved by integer programming (IP). In this thesis, two suboptimal methods are proposed. First method considers two types of users simultaneously in subcarrier allocation algorithm and is similar to the previous work which was adaptive modulation for maximum data rate with single types of users using linear programming. In second method, subcarriers are allocated successively. The amount of computations can be reduced when fixed data rate is small with little performance degradation. We verify the effectiveness of our proposed method by Computer simulation results and complexity comparisons.