A novel technique, directly using artificial neural networks, is proposed for the adaptive control of nonlinear systems. The ability of neural networks to model arbitrary nonlinear functions and their inverses is exploited. The use of nonlinear function inverses raises questions of the existence of the inverse operators. These are investigated and results are given characterising the invertibility of a class of nonlinear dynamical systems. The control structure used is internal model control. It is used to directly incorporate networks modelling the plant and its inverse within the control strategy. The potential of the proposed method is demonstrated by an example.