The applicability of and relationship between two rate-independent hysteresis models that have been used to describe hysteresis in piezoceramic transducers are investigated. It is shown that the generalized Maxwell resistive capacitor hysteresis model is a particular case of the classical Preisach hysteresis model. The Preisach function that reduces the Preisach model to the Maxwell resistive capacitor model is derived. It is also shown that the inverse of the Maxwell model is this same particular case of the classical Preisach model. A Maxwell model identification procedure based on Preisach identification principles is formulated. The applicability of the classical Preisach and Maxwell hysteresis models for identifying and simulating piezoceramic dielectric behavior is investigated experimentally via studies on a 1-3 piezoceramic composite. Results indicate that both hysteresis models can accurately represent piezoceramic hysteresis. It is noted that the identified relationship between Preisach and Maxwell hysteresis models may prove useful in a wider range of hysteresis applications than just those involving piezoceramics.