The paper deals with the identification of nonlinear systems described by the nonlinear difference equations of the certain type. These equations are known in literature dealing with the systems modelling by means of neural network as the models of the second type. In some cases, when these models are nonlinear also in parameters and we want to use the least square method for parameter estimation, it is necessary to transform the models into linear forms. Our attention has chiefly been paid to the practical utilization of the proposed algorithm and to this verification on simulated example.