We first derive a necessary condition and a sufficient condition in terms of steady-state input-output relations for the integral controllability of uncertain nonlinear systems. A simple nonlinear integral controller is constructed for asymptotically stabilizing a set of nonlinear systems. We then propose a computationally efficient Nonlinear Model Predictive Control algorithm for the control of large-scale constrained nonlinear systems. The algorithm consists of two levels and uses a closed-loop control strategy. The simple integral controller is used as the lower-level controller and can be tuned to guarantee robust asymptotic stability. The higher-level controller optimizes nominal performance subject to a robust stability constraint and an on-line computational time constraint. The stability results do not require that a global optimal solution be found.