A method of representation and optimization of a class of non-linear systems far which the input and the output are ergodic random processes is presented. In this method the system, is realized as a cascade combination of a single-input-multi-output linear system followed by a multi-input-single-output non-linear no-memory system. The linear part of the system is such that its memory pattern can be adjusted as desired. The non-linear no-memory part is a piecewise multilinear function of its inputs. This model is then used to optimize the system with a minimum weighted moan-square error criterion. This method of optimization is independent of the statistics of the input. A method of synthesis of the optimum system thus obtained is presented also.