This paper proposes a nonlinear system identification using parallel linear-plus-neural network models that provide more accurate predictions on the process behavior even on extrapolated regions. For this purpose, a residuals-based identification algorithm using parallel integration of linear orthonormal basis filters (OBF) and neural networks model is developed and analyzed under range extrapolations. Results on the van de Vusse reactor case study show enhanced extrapolation capability when compared to the conventional neural network (NN) and the series Wiener-NN models. © 2013 Elsevier Ltd.