The paper investigates the application of inversion of a radial basis function network (RBFN) to nonlinear control problems for which the structure of the nonlinearity is unknown. Initially, the RBF network is trained to learn the forward dynamics of the plant. Two different controller structures are then proposed based on this identified RBFN model. In one scheme, a feedback control law is derived based on the input prediction by inversion of the RBFN model so that the system is Lyapunov stable. The second kind of controller structure predicts the feedforward control action, while the fixed controller actuates the feedback stabilising signal. An extended Kalman filtering based algorithm is employed to carry out the network inversion during each sampling interval. Two examples are presented to verify the proposed scheme. Simulation results show that the performance of the controller based on the proposed network inversion scheme is efficient.