AbstractHysteresis operators have recently proved to be a powerful tool in modelling phase transition phenomena which are accompanied by the occurrence of hysteresis effects. In a series of papers, the present authors have proposed phase‐field models in which hysteresis non‐linearities occur at several places. A very important class of hysteresis operators studied in this connection is formed by the so‐called Prandtl–Ishlinskii operators. For these operators, the corresponding phase‐field systems are in the multi‐dimensional case only known to admit unique solutions if the characteristic convex sets defining the operators are polyhedrons. In this paper, we use approximation techniques to extend the known results to multi‐dimensional Prandtl–Ishlinskii operators having non‐polyhedral convex characteristicsets. Copyright © 2002 John Wiley & Sons, Ltd.