This paper is concerned with the global stabilization of multiple integrator systems subjected to input saturation. Among the existing works, nested saturation method has been demonstrated to be an effective tool. In the present contribution, an adaptive nested saturation feedback law is proposed which takes the advantages of time varying parameters in the saturation functions along with employing the well-known extended state observer. The global stability of the proposed approach for a desired order of integrators' chain is demonstrated. The performance of the proposed control law is compared with the existing methods in the case of a triple integrator chain. It is shown that the proposed approach significantly improves the transient and steady state performance of closed-loop system at the presence of external disturbances. (C) 2018 Elsevier Ltd. All rights reserved.