In this paper, we propose a model for dynamic magnetostrictive hysteresisin a thin rod actuator. We derive two equations that representmagnetic and mechanical dynamic equilibrium. Our model results from an application of the energy balance principle.It is a dynamic model as it accounts for inertial effects and mechanicaldissipation as the actuator deforms, and also eddy current lossesin the ferromagnetic material. We show rigorously that the model admits a periodic solution thatis asymptotically stable when a periodic forcing function is applied.(Proc. Conf. Information Sci. and Systems, Princeton, March 1998)