In this brief, we propose a dynamic surface control with actuator failure compensation for a class of feedback linearizable systems with locally Lipschitz nonlinearities. First, a dynamic surface state feedback control scheme is designed, which incorporates radial basis function networks in a novel approach, to compensate system uncertainties and dynamic changes induced by actuator failures. Then, an output feedback controller is obtained by means of high-gain observers. It is proved that our control schemes guarantee the uniform ultimate boundedness of the system, and that the output tracking error converges to an arbitrarily small residual set. Finally, a simulation is carried out to illustrate the performance of the designed control schemes.