This paper studies the problem of global robust H-infinity disturbance attenuation for a class of non-minimum-phase nonlinear systems subject to parameter uncertainty. The problem addressed is the design of a state feedback controller such that the closed-loop system is input-to-state stable and the L-2-gain from the disturbance input to the controlled output is not larger than a prescribed value for all admissible parameter uncertainties. A recursive Lyapunov-based design approach is developed to construct the controller explicitly. The problem of global robust H-infinity almost disturbance decoupling, where the level of disturbance attenuation can be made arbitrarily small for all allowed uncertainties, is also addressed.