A feed and cutting device for dividing a continuous web into portions is described. The device comprises along a feed plane, guiding device for the web comprising a pair of mutually tangential rollers, apparatus for feeding the web along said plane and a device for cutting the web into portions. The main feature of the device is that at least one of the guide rollers is mounted on a shaft coaxial thereto and rotating with continuous motion, and is connected to the shaft by a self-locking device which prohibits any discordant relative rotation between the roller and the shaft but which allows idle rotation of the roller on the shaft at an angular speed exceeding the angular speed of the shaft, the angular speed of the shaft being close to but less than the angular speed transmitted to the respective roller by the feed device by way of said web.