This note studies min-max systems which are dynamic systems involving three operations (min, max, +). We present a feedback stabilization policy for a class of min-max systems such that the closed-loop systems have a global cycle time which is the same as the maximal Lyapunov exponent of the open-loop systems. Our results are based on structural properties of min-max systems. (C) 2003 Elsevier Science Ltd. All rights reserved.