A workpiece being processed on a machine tool is moved by control devices to the tool head or work station of the machine mechanically or automatically. A stop defines an area around the work station from which the holding devices must be kept to prevent damage. As soon as a holding device reaches the limit of the danger zone around the tool head, it is switched into a setting releasing the workpiece and moves into a position away from the work station. The machine has a switching element connected to each holding device to be so movable, and the switching element has a switching slide which is acted on by an applied force and is supported in a first position until it abuts the stop when one slide position connects the energy source to the drive of the holding device to move it away from the stop. In another slide position, the connection to the energy source is broken and the holding device returns to the workpiece holding position.