A sliver processing machine includes a plurality of roll pairs between which a running sliver passes. Each roll pair is composed of a driving roll and a pressure roll. A separate pressing device is connected with each pressure roll for urging each pressure roll against its driving roll. Each pressing device has a shiftable element displaced by the pressure roll upon radial displacement of the pressure roll in response to winding of sliver on either the pressure roll or the associated driving roll. A common actuating element is connected to each shiftable element of each pressing device for displacing the common actuating element upon displacement of any one of the shiftable elements. A switching device is connected to the common actuating element. The switching device has an idle state and a signal-generating state. The switching device is placed into the signal-generating state by the common actuating element upon displacement of the common actuating element by any one of the shiftable elements, whereby the switching device generates a signal in response to winding of sliver on any roll of any of the roll pairs.