The problem of H-infinity-estimation for uncertain discrete-time, nonlinear systems with nonlinear time-varying parameter uncertainty is investigated. A discrete-time nonlinear estimator is introduced so that an H-infinity-norm-like measure of the estimation error is guaranteed to be bounded by a prescribed level, for all admissible uncertainties. An auxiliary estimation problem is considered which results from the original estimation problem by converting the family of norm-bounded parameter uncertainties into a set of exogenous energy bounded signals. Sufficient conditions for the existence of an H-infinity nonlinear estimator for the auxiliary problem are obtained, and it is shown that the resulting estimator, if it exists, guarantees the required performance when applied to the original problem for all the admissible parameters.