This paper revisits the stability issue of earlier model predictive control (MPC) algorithms where the performance index has a finite receding horizon and there is no terminal penalty in the performance index or other constraints added in online optimisation for the purpose of stability. Stability conditions are presented for MPC of constrained linear and nonlinear systems,and there is no restriction on the length of the horizon. These conditions can be used to test whether or not desired stability properties can be achieved under chosen state and control weightings.