WiMax is one of the most important technologies for providing a broadband wireless access (BWA) in a metropolitan area. The use of OFDM transmissions has been proposed to reduce the effect of multipath fading in wireless communications. Moreover, multiple access is achieved by resorting to the OFDMA scheme. Adaptive subcarrier allocation techniques have been selected to exploit the multiuser diversity, leading to an improvement of performance by assigning subchannels to the users accordingly with their channel conditions. A method to allocate subcarriers is to assign almost an equal bandwidth to all users (fair allocation). However, it is well known that this method limits the bandwidth efficiency of the system. In order to lower this drawback, in this paper, two different adaptive subcarrier allocation algorithms are proposed and analyzed. Their aim is to share the network bandwidth among users on the basis of specific channel conditions without loosing bandwidth efficiency and fairness. Performance comparisons with the static and the fair allocation approaches are presented in terms of bit error rate and throughput to highlight the better behavior of the proposed schemes in particular when users have different distances from the BS.