Abstract: For systems with input saturation constraint and invertible static input nonlinearity, a two step generalized predictive control (TSGPC) strategy is adopted. An intermediate variable representing the desired control action is obtained by applying linear GPC (LGPC), then the invertible static nonlinearity is compensated by solving nonlinear algebraic equation (NAE) and the input saturation constraint is satisfied by desaturation. TSGPC has low computational burden and is especially suitable for fast control application. The closed-loop block diagram of this system is turned into a static nonlinear feedback form, and Popov's theorem is applied to the closed-loop stability analysis. The sufficient stability conditions are obtained. Effective algorithms for determining controller parameters are given to make the stability conclusions applicable and an example is given for illustration.