In this paper a predictive control algorithm for nonlinear discrete-time systems is presented. Starting from a state-space model, conditions for the asymptotic tracking of constant reference signals in a neighbourhood of a given equilibrium are first derived. Then it is shown that the system under control can be locally described in terms of a suitable NARX (Nonlinear ARX) model, which, in practice, can be identified by means of well-established techniques. For the NARX model, a receding-horizon predictive control algorithm is proposed which guarantees local stability and robust asymptotic tracking in the neighbourhood of the equilibrium. Conditions for local stability and tracking are given in terms of reachability, observability and transmission zeros of the linearization of the original state-space system around the equilibrium. An example is reported to illustrate the effectiveness of the proposed method.