Nonlinear H-infinity-controller synthesis is presented for time-varying systems via sampled-data measurement feedback. The H-infinity-control problem for a nonlinear system with a sampled-data measurement output is shown to be equivalent to the H-infinity-control problem for a certain nonlinear system with a time-continuous measurement output. Special mathematical tools are developed to straightforwardly derive a local solution of the sampled-data measurement feedback (SMF) H-infinity-control problem from that of the time-continuous measurement feedback. (CRLF) H-infinity-control problem.