This paper investigates the problem of robust H-infinity-output feedback control for nonlinear systems with time-varying parameter uncertainty satisfying some integral functional constraints. We address the problem of designing a compensator such that the L(2)-gain of the mapping from the exogenous input noise to the penalty output is minimized or guaranteed to be less than or equal to a prescribed value. We establish the interconnection between the robust nonlinear H-infinity-control problem and the nonlinear H-infinity-control problem. Based on this connection, a sufficient condition for the existence of a solution to the robust nonlinear H-infinity-output feedback control problem is derived in terms of a "scaled" Hamilton-Jacobi inequality.