A labelling machine for labelling containers may include at least a container feed means, a labelling region, a container removal means, and at least one labelling unit for processing labels from the roll. The labelling unit may comprise at least one label roll, a label feeder, a cutting device, a gripper cylinder, and at least one gluing mechanism. The cutting device may be constituted by a rotating vacuum roller and a rotating parting element which, on its circumference, has at least one parting tool, for example, a cutting blade, and the cutting device may be held by a common support device having, at least, a base part and a cover part. The support device has the same mean coefficient of thermal expansion as the rotating vacuum roller and the rotating parting element.