The problem of efficient nonlinear model predictive control (NMPC) implementation is investigated, using an approximating function Â¿Â¿ to avoid on-line optimization. At first, sufficient conditions are given for Â¿Â¿ to guarantee a finite computable bound on the approximation error (i.e. the difference between the exact and approximated control moves). Then, additional conditions are obtained to make such a bound arbitrary small. This result makes it possible to derive guaranteed closed loop stability properties. Finally, it is shown that set membership (SM) nonlinear function approximation theory can be employed to improve the performance of Â¿Â¿. The resulting Â¿fastÂ¿ model predictive control law is given by the sum of Â¿Â¿ with a SM approximated function and satisfies the above-mentioned conditions even if they are not met by Â¿Â¿ alone. A nonlinear oscillator example shows the effectiveness of the proposed methodology.