Artificial neural networks (ANNs) have been used to construct empirical nonlinear models of process data. Because networks are not based on the physical theory and contain nonlinearities, their predictions are suspect when extrapolating beyond the range of original training data. Standard networks give no indication of possible errors due to extrapolation. This paper describes a sequential supervised learning scheme for the recently formalized Growing Multi-experts Network (GMN). It is shown that the Certainty Factor can be generated by the GMN that can be taken as an extrapolation detector for the GMN. The On-line GMN identification algorithm is presented and its performance is evaluated. The capability of the GMN to extrapolate is also indicated. Four benchmark experiments are dealt with to demonstrate the effectiveness and utility of the GMN as a universal function approximator.