The current optimal joint rate and power control algorithms for wireless networks are mainly for elastic traffic which has strictly concave utility functions. In the multiclass service networks such that elastic and inelastic, the inelastic traffic is usually associated with the sigmoidal utilities which are nonconcave functions. Therefore, the corresponding Network Utility Maximization (NUM) problem is nonconvex in both objective and constraints. The current approaches cannot be applied and the problem is difficult to solve for the global optimal solution even with the centralized method. This paper proposes the joint rate and power control algorithm which can be distributively implemented. We approximate the nonconvex NUM to the convex problem which is easily solved by dual decomposition method. After a series of approximations, the algorithm converges the local optimal solution.