Several paradigms are available for developing nonlinear dynamic input-output models of processes. Polynomial models, threshold models, models based on spline functions, and polynomial models with exponential and trigonometric functions can describe various types of nonlinearities and pathological behavior observed in many physical processes. A unified nonlinear model development framework is not available, and the search of the appropriate nonlinear structure is part of the model development effort. Various artificial neural network structures and nonlinear time series model structures are presented and illustrated by developing a model from data sets generated by a series of example systems. The use of a nonlinear model development paradigm which is not compatible with the types of nonlinearities that exist in the data can have a significant effect on model development effort and model accuracy.