This paper is concerned with the problem of robust stabilisation of multiple integrators systems subject to input saturation and disturbance from the viewpoint of state feedback and output feedback. First of all, without considering the disturbance, a backstepping-like method in conjunction with a series of saturation functions with different saturation levels is employed to design a nested-saturation based state-feedback controller with pre-chosen parameters. On this basis, taking the disturbance into account, a sliding mode disturbance observer (DOB) is adopted to estimate the states and the disturbance. Then, by combining the above state-feedback controller and the estimated states together, a composite controller with disturbance compensation is developed. With the removal of the non-increasing restriction on the saturation levels, the controller design becomes very flexible and the convergence performance of the closed-loop system is much improved. Meanwhile, with the aid of the estimated values by the DOB, we obtain not only the output-feedback control scheme but also the better disturbance rejection property for the closed-loop system. A simulation example of a triple integrators system is presented to substantiate the usefulness of the proposed technique.