This paper addresses the stability problem for a set of switched nonlinear difference equations with parametric uncertainties. For the corresponding family of subsystems, a regularization procedure is suggested, and a multiple Lyapunov function is constructed. With the aid of the Lyapunov function, classes of switching signals are determined for which the asymptotic stability of a stationary solution of a given set of equations may be guaranteed. An application of the proposed approach to the stability analysis of multiconnected switched difference systems by nonlinear approximation is presented. An example is given to illustrate our results.