Cutting device for longitudinally cutting a film web, in particular a plastic film web, moved in a web plane in a transport direction into a plurality of film bands, wherein a first cutter bar provided with cutting blades is immersed with the cutting blades in a cutting position into the web plane. In order to replace the cutter bar, a second cutter bar provided with cutting blades may be immersed with its cutting blades into the web plane, wherein the first cutter bar may be moved from the cutting position into a transfer position outside of the web plane when the second cutter bar is immersed with its cutting blades into the web plane.