Resource allocation is expected to be a most important factor especially for heterogeneous applications in wireless ad hoc networks. In this paper, a novel heterogeneous resource allocation algorithm (HRA) is presented for ad hoc networks, supporting both elastic and inelastic traffic. First, by combining the first order Lagrangian method with pseudo utility, the original nonconvex problem is converted into a new convex one. Then, we successfully solve the heterogeneous problem with the dual-based decomposition approach. In addition, we integrate utility fairness into the resource allocation framework, which can adaptively manage the tradeoff between elastic and inelastic flows. Simulations show and prove that HRA converges fast and can achieve the global optimum starting from many different network conditions, such as elastic, inelastic, and hybrid scenario. With both considerations of flow rate and utility fairness, HRA improves the overall network utility and system throughput greatly.