A wireless resource allocation algorithm based on utility functions is presented. Distinct utility functions dependent on the specific traffic class and the numerical QoS requirements are combined and maximised, so that different treatment is provided to each data flow. This approach is applied to allocate subcarriers and slots of an adaptive OFDMA scheme for services with heterogeneous QoS requirements quantified as delay, jitter or throughput. A tradeoff between services' needs can be reached by the proposed utility based scheme, instead of the maximum aggregated throughput achieved by the traditional best channel allocation algorithm.