A compensation scheme is presented for general nonlinear actuator deadzones of unknown width. The compensator uses two neural networks (NN's), one to estimate the unknown deadzone and another to provide adaptive compensation in the feedforward path, The compensator NN has a special augmented form containing extra neurons whose activation functions provide a "jump function basis set" for approximating piecewise continuous functions. Rigorous proofs of closed-loop stability for the deadzone compensator are provided and yield tuning algorithms for the weights of the two NN's, The technique provides a general procedure for using NN's to determine the preinverse of an unknown right-invertible function.