Many authors have noted the difficulty of developing the models required for nonlinear model predictive control (NMPC) and other nonlinear, model-based control strategies. One reason this task is difficult is that success depends strongly on initially selecting a reasonable structure for this nonlinear model. Unfortunately, this selection is extremely difficult because most of our intuition about structure/behavior relations (e.g., if the step response exhibits overshoot, a model of at least second order is required) is based on experience with relatively low-order linear models and often fails completely when confronted with comparably simple nonlinear models. To help bridge this chasm between nonlinear model behavior and our linear intuition, this paper describes some broad classes of nonlinear model structures, which may be approximately characterized as mildly nonlinear, strongly nonlinear, or of intermediate nonlinearity, depending on the different ways they violate linear intuition. It is hoped that these results will be useful in selecting simple nonlinear model structures for use in model-based control.