In this paper, the authors consider the standard H-infinity-control problem far more general nonlinear systems modeled by equations in which the penalty output z and the measured output y are, in general, functions of the state x, the exogenous input w, and the control input u. In particular, we characterize a family of H-infinity controllers via output feedback as well as state feedback, solving the problem. The results obtained in this paper generalize some recent results in the literature.