This paper introduces a new systematic methodology to the problem of nonlinear system identification with the aid of neural networks, fuzzy systems and truncated Chebyshev series. The proposed methodology is of general use and results in both a linguistic and an analytical model of the system under study. The method was successfully tested in the identification of certain operating regions in a Continuous Stirred Tank Reactor (CSTR) exhibiting various types of nonlinear behaviour, such as limit cycles and multiple steady states. The performance of the methodology was evaluated via a comparison with two different identification schemes, namely a feedforward neural network and an approach based on the normal form theory.