Abstract: An apparatus for the adjustment of the tension in rotating gripping devices, which are operable with variable power outputs and follow (hysteresis) distinct tension-characteristics for build-up and withdrawal. In order to make possible a stabilization of the tension which is independent from the rotational speed, a desired value for the tension and an internal tolerance allotment for an upper and a lower desired adjustment value are presupposed in a control apparatus. In the control apparatus a leading regulated quantity is produced digitally for the changing of power outputs. The leading regulated quantity is reduced when the desired value approaches a presupposed amount, so that the actual value in presupposed intervals lessens regularly through the regulated quantity reduction under the desired value and is again increased.