A novel approach based on a nonlinear compensator is proposed to prevent 'windup', which is caused by the saturation of the actuator and the integral action of the controller. The anti-windup compensator is located between the conventional linear controller, designed neglecting the saturation, and the actuator. It was proven based on the describing function method that, if the closed loop control systems are stable assuming no saturation, then there exist a range of compensator gain which prevents any limit-cycle and hence, guarantees the system stability. The computer simulation results show that the compensator proposed in the manuscript can eliminate unstable limit cycle and improve the transient response. The proposed anti-windup compensator can be applied not only to SISO control systems but also to MIMO control systems because the compensator can be designed and implemented independently from the controllers. In addition to 'windup', the anti-windup compensator prevents 'jump-resonance', which is a nonlinear phenomenon caused by saturation. The computer simulation results also show that the anti-windup compensator prevents 'windup' and 'jump-resonance'.