The winding belt (1) which is wound from a supply reel (2) onto a winding core (3) is used at the same time as the drive belt for the winding core. It is first provided as the under belt and then after one revolution of the winding core takes over the function of the upper belt for the next layer which is to be wound up. The winding belt can be drawn off from the belt supply reel (2) by a drive belt (5) driven by a drive. It is then directed over a turning roller (13) and belt feed roller (7) and from there to the winding core which is turning anticlockwise. The drive motor, winding core and guide devices for the winding belt are mounted on a frame (23).