The finite time horizon H-infinity-control problems for nonlinear time-varying systems are considered where the initial state is unknown. They are solved by using both static state feedback and dynamic output feedback controllers. A class of nonlinear H-infinity- controllers is parameterized as nonlinear fractional transformation on contractive nonlinear parameters. The solvability for nonlinear finite time horizon H-infinity-control problem requires suitable solutions to some Hamilton-Jacobi inequalities (equations).