It is shown that there exists an analytic solution to the discrete Hamilton-Jacobi equation arising in the nonlinear discrete-time H-infinity-control problem if and only if the H-infinity-control problem associated to the linear approximated system is solvable. Starting from the solution of the Riccati equation associated to this linear problem, we show that the nonlinear solution can be computed at any desired degree of approximation, On this basis the control solution can be computed iteratively.