Repetitive controllers are generally applied to reject periodic disturbances and to track periodic reference signals with a known period. Their design is based on the internal model principle, proposed by Francis and Wonham (1975). This paper describes a new finite-dimensional SISO repetitive controller for two different classes of nonlinear plants. Simulation results show asymptotic tracking of the periodic reference signal by the proposed repetitive controller in closed loop up to the Nth harmonic frequency. A proof of robustness of the repetitive control system to small nonlinearities, like actuator nonlinearities, is provided.