The receding-horizon (RH) methodology is extended to the design of a robust controller of H-infinity type for nonlinear systems. Using the nonlinear analogue of the Fake H-infinity algebraic Riccati equation, we derive an inverse optimality result for the RH schemes for which increasing the horizon causes a decrease of the optimal cost function. This inverse optimality result shows that the input-output map of the closed-loop system obtained with the RH control law has a bounded L-2-gain. Robustness properties of the nonlinear H-infinity control law in face of dynamic input uncertainty are considered.