This paper explores the role of structural change in systems of demand equations. Specifically, we adapt the time—varying regression framework of Lin and Teräsvirta (1994), which in turn is related to the dynamic smooth transition models introduced by Teräsvirta (1994). Unlike previous efforts at modeling structural change in demand systems, we do not impose the nature of the change to be monotonic—several non-monotonic alternatives are considered. An application is presented using the Almost Ideal Inverse Demand System (IAIDS) applied to U.S. meat demand data, 1960-2004. Results show the importance of modeling structural change and that, moreover, the best-fitting model is associated with a form of symmetric, non-monotonic structural change.