Systems described by state difference equations containing small parameters nrc cast. into singularly perturbed form. A perturbation method is developed t.o obtain an approximnte solut-ion conaist-ing of all outer series and a correction series. The characterisric features of singular perturbations UfC clearly brought. onto Duo to the interplay between the various steps involved in the actual working of the method, an algorithm is presented. Examples are given to illustrate the method.