In this paper, a two-dimensional automatic control system containing a single nonlinear hysteresis element of the general form is considered. Such systems represent mathematical models for real control systems, and have been considered in many papers on the subject. A system phase space, which is a manifold with boundary, is established. The conditions needed for the considered system to be globally stable, in a certain sense, are derived. A notion of ”sliding mode” is used in this paper. Refs 16. Figs 4.