Practical difficulties involved in implementing stabilizing model predictive control laws for nonlinear systems are well known, Stabilizing formulations of the method normally rely on the assumption that global and exact solutions of nonconvex, nonlinear optimization problems are possible in limited computational time, In this paper, we first establish conditions under which suboptimal model predictive control (MPC) controllers are stabilizing; the conditions are mild holding out the hope that many existing controllers remain stabilizing even if optimality is lost. Second, we present and analyze two suboptimal MPC schemes that are guaranteed to be stabilizing, provided an Initial feasible solution is available and fur which the computational requirements are more reasonable.