Apparatus and process for winding a material web into a wound roll on a winding core. The apparatus includes a press roll, movable press roll bearings coupled to the press roll, and a pressing device positioned to press the press roll against the wound roll. In this manner, the press roll and the wound roll form a winding nip, and the material web is guided the press roll and through the winding nip. The pressing device is adapted to set a line load in the winding nip, and movable winding core bearings are couplable to the winding core of the wound roll and are adapted to move the winding core to compensate for an increasing wound roll diameter. The winding nip one of remains in an at least approximately same position and is displaced by a small amount during winding. A driving device is positioned to move each of the movable winding core bearings, and a control device is arranged to control the driving device as a function of movement of the press roll from a desired position. A position measurement device, coupled to at least one of the movable press roll bearings, is adapted to produce an instantaneous position value of the press roll in accordance with a current position of the press roll, a regulator is adapted to compare the instantaneous position value with a desired position value of the press roll and to transmit an actuating variable that corresponds to a deviation of the instantaneous value from the desired value, and a wire is adapted to transmit the actuating variable from the regulator to the control device.