This paper is concerned with the finite-horizon estimation problem of randomly occurring faults for a class of nonlinear systems whose parameters are all time-varying. The faults are assumed to occur in a random way governed by two sets of Bernoulli distributed white sequences. The stochastic nonlinearities entering the system are described by statistical means that can cover several classes of well-studied nonlinearities. The aim of the problem is to estimate the random faults, over a finite horizon, such that the influence from the exogenous disturbances onto the estimation errors is attenuated at the given level quantified by an H-infinity-norm in the mean square sense. By using the completing squares method and stochastic analysis techniques, necessary and sufficient conditions are established for the existence of the desired finitehorizon H-infinity fault estimator whose parameters are then obtained by solving coupled backward recursive Riccati difference equations (RDEs). A simulation example is utilized to illustrate the effectiveness of the proposed fault estimation method. (C) 2014 Elsevier Ltd. All rights reserved.