The global stabilization problem of the multiple-integrator system by bounded controls is considered. A nonlinear feedback law consisting of nested saturation functions is proposed. This type of nonlinear feedback law that is a modification and generalization of the result given in [1] needs only [(n + 1)/2] (n is the dimensions of the system) saturation elements,which is fewer than that which the other nonlinear laws need. Furthermore,the poles of the closed-loop system can be placed on any location on the left real axis when none of the saturation elements in the control laws is saturated. This type of nonlinear control law exhibits a simpler structure and can significantly improve the transient performances of the closed-loop system,and is very superior to the other existing methods. Simulation on a fourth-order system is used to validate the proposed method. The global stabilization problem of the multiple-integrator system by bounded controls is considered. A nonlinear feedback law consisting of nested saturation functions is proposed. This type of nonlinear feedback law that is a modification and generalization of the result given in [1] needs only [n + 1) / 2] (n is the dimensions of the system) saturation elements, which is fewer than that of which the other nonlinear law need. Furthermore, the poles of the closed-loop system can be placed on any location on This type of nonlinear control law exhibits a simpler structure and can significantly significantly improve the transient performances of the closed-loop system, and is very superior to the other existing methods Simulation on a fourth-order system is used to validate the proposed method.