Abstract: Cutting device (1) for lengthwise cutting of a moving, flexible web (2) containing an initial knife pulley (4), a second knife pulley (6) and a cylinder (11) with a moving piston (13), said second knife pulley being adjustable relative to the first knife pulley subject to the compressive force from the piston to bring the edge of the second knife pulley (10) to work with the edge of the first knife pulley (9). According to the invention, the cutting device has a slide (14) that is situated between the second knife pulley and the cylinder, said slide being adjustable in the axial direction of the second knife pulley and connected to the piston to follow its movement, and in which slide the second knife pulley has been rotatively stored.