Hysteresis of smart devices should be modeled in order to improve the performances and to relieve the control system tasks. Prandtl–Ishlinskiı˘ (PI) and Generalized Prandtl–Ishlinskiı˘ (GPI) hysteresis operators are popular because of their easiness of implementation and of the availability of inverse closed formulas. Nevertheless, PI and GPI are a subset of Preisach model (PM). Therefore, in principle, they are limited in representing hysteretic behaviors with respect to PM. In this paper, a first attempt to study the representation error of GPI with respect to general Preisach hysteretic behavior is presented and evaluated through two numerical experiments.