A cutting device is used to accomplish the transverse cutting of at least a first material web. The cutting device includes a cutting cylinder and a first counter cylinder. These two cylinders rotate cooperatively and define a first gap through what a first transport path for the first web runs. The cutting cylinder has at least one cutting blade, that cuts a product off the web passing through the gap. The cutting cylinder also has a holding device for holding a cut product and for transporting it through the gap. The counter cylinder comprises a thrust bearing cooperating with the cutting blade.