The disturbance suppression problem for nonlinear systems is examined in this paper. We review the so-called nonstandard mixed sensitivity problem, which introduces an integrator to a selected weight, as well as the linear classical disturbance suppression problem and the linear H-infinity disturbance suppression problem. We extend this H-infinity problem to the nonlinear case, and present a method to reduce the order of the state feedback Hamilton-Jacobi (HJ) partial differential equation for this nonlinear H-infinity problem by extending the concept of comprehensive stability (Proceedings of the 36th Conference on Decision and Control, 1997, p. 4653; IEEE Trans. Ind. Electron. (1998) 488). Finally, we investigate the structure of the output feedback H-infinity controller for disturbance suppression, and draw the conclusion that, as in the linear case, there must also be an integrator in the controller.