In this paper an identification algorithm for a special model class which captures essential characteristics of many nonlinear systems is presented. Conditions are given under which this nonlinear model can be identified by use of efficient linear tools. Subspace identification is used here to determine the linear part of the model and an initial estimate for the nonlinear one. The estimate of the nonlinear part is computed by a final numerical optimization step. A simulation study illustrates the applicability of the proposed method.