Abstract
Theoretical investigation of the magnetisation process in high-spin cluster is performed. The source of hysteresis is studied; magnetisation jumps on hysteresis loops of a cluster corresponding to intersections of energy levels are described theoretically. An analytical formula for the dependence of the height of a jump on the sweeping rate of external field is obtained. It is shown that the width of a jump is crucially influenced by fluctuating fields produced by the cluster environment.