The structure of NARMAX models is described. No new algorithm for structure selection is proposed, but rather the paper investigates how different model structures are produced by a large class of nonlinearities in the system which generates the data. The concept of term clusters is used to understand how different types of terms are required to model nonlinear systems. A term cluster generating mechanism is suggested, this can be used not only to understand how certain types of terms appear in NARMAX models but also, in the case of prior knowledge, such a mechanism can serve as an aid to select the structure of nonlinear models. The results are quite general and can be applied to polynomial, rational and extended-set NARMAX representations.