A device for winding a web, preferably a plastic film web produced in a blowing or casting process, includes a driven winding tube for a web, a web tension measuring roller, a driven contact roller positioned between the winding tube and the web tension measuring roller which, in the case of contact winding, can be positioned against the film roll being formed and which, in the case of gap winding, is positioned at a distance from the film roll. A control device controls the motors as a function of the feeding speed of the web and in accordance with the measured tractive force of the web, such that the coil hardness of the wound roll can be predetermined. In the case of contact winding, the torque of the winding motor is controlled according to the increasing diameter of the wound roll and the contact roller is driven at a speed that is controlled according to the tractive force of the web. In the case of gap winding, the speed of the winding motor is controlled according to the measured tractive force of the web.