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Volterra series are known to be efficient to represent weakly nonlinear systems and take into account the first distortions. Their truncated versions allow to derive realizations (in the sense of system theory) leading to networks composed of linear filters, sums and instantaneous products of signals, without instantaneous feedback loops, from which low cost digital simulations are obtained. Nevertheless, if saturation phenomena arise, truncating the series at low order is not sufficient and the convergence can also be lost. This paper introduces a change of state which preserves the efficiency of Volterra series expansions in such a case, even at a very low truncation order. The deduced digital system to simulate preserves the properties mentioned above and includes two delay lines (possibly of 1 sample) and a nonlinear (static) function, given by the method.