In this paper, a two-dimensional automatic control system containing a single nonlinear hysteresis element of the general form is considered. Phase space of the system is a manifold with boundary consisting of two connected sheets. Existence of manifold boundary is conditioned by the motion of the phase point along hysteresis loop. This work is a continuation of the paper “Conditions for the global stability of a single system with hysteresis nonlinearity” published previously by the authors, where it is shown that under some conditions on the functions defining hysteresis such system is in a way globally stable. This paper presents sufficient conditions for considered system to have at least two limit cycles. Three closed contours embedded into each other are constructed in order to prove the existence of cycles on the phase manifold. The contours are composed of the pieces of the level lines of various Lyapunov functions. The inner contour is crossed by system trajectories from the outside to the inside, the middle contour is crossed by the trajectories from the inside to the outside. The outer contour is crossed by the system trajectories from the outside to the inside. The existence of such contours proves the presence of at least two limit cycles in the system.