Abstract: An apparatus for continuously winding a web of sheet material into rolls comprises a turret mechanism (1) comprising two or more winding mandrels (2,3,4,5). The turret mechanism (1) is rotatably indexed to bring each mandrel (2,3,4,5) in turn into a winding position in which it is rotatably driven to wind a web of sheet material (8) connected thereto into a roll, and to bring the adjacent mandrel lying immediately behind it in the direction of rotation of the turret into contact with the web (8). The adjacent mandrel is rotatable. Rotary element (11) is adapted for selective engagement with the adjacent mandrel, which rotary element (11) is rotatably driven in the opposite direction to the adjacent mandrel and at a greater speed. The apparatus further comprises a web cutting mechanism (16) adapted to cut the web (8) at a point lying between the current rewind mandrel and the adjacent mandrel.