Predictive control of nonlinear systems subject to state and input constraints is considered. Given an auxiliary linear control law, a good nonlinear receding-horizon controller should (i) be computationally feasible, (ii) enlarge the stability region of the auxiliary controller, and (iii) approximate the optimal nonlinear infinite-horizon controller in a neighbourhood of the equilibrium. The proposed scheme achieves these objectives by using a prediction horizon longer than the control one in the finite-horizon cost function. This means that optimization is carried out only with respect to the first few input moves whereas the state movement is predicted (and penalized) over a longer horizon where the remaining input moves are computed using the auxiliary linear control law. Closed-loop stability is ensured by means of a penalty on the terminal state which is a computable approximation of the infinite-horizon cost associated with the auxiliary controller. As an illustrative example, the predictive control of a highly nonlinear chemical reactor is discussed.