Abstract: A method and an apparatus for winding or rewinding a running web onto the center core shafts of rolls. While the running web is being wound, at a selected speed, onto a first roll which is, disposed in an operating position, a center core shaft of a new, second roll is disposed in a splicing position so that the center core shafts are side by side and adjacent to each other. A fixed drive assembly and a movable drive assembly control the speeds of the first and second rolls, respectively. The first roll has had a determined amount of web wound thereon, the running web is spliced onto the center core shaft of the second roll and thereafter is wound onto the second roll. Thereafter, the second roll is disconnected from the fixed drive assembly and is removed from the operating position. The second roll, with the running web now being wound thereon, is then moved, with the movable drive assembly, from the splicing position to the operation position.