Abstract: The winder comprises a central driving carrier tube (1) and winding drums (2) equipped with self-blocking systems (3) for receiving reeling mandrils (4) arranged successively round the central driving carrier tube, the said drums (2) each being connected to this tube by means of a magnetic coupling (16), (17), (18) located inside the said tube (1) and connected, on the one hand, rigidly to this tube (1) and, on the other hand, to the drum (2), in said winder the connection between the magnetic coupling (16), (17), (18) and the drum (2) being made via a speed multiplier (6), (6'), (6"), (13) likewise arranged in the central driving carrier tube (1). The winder allows a reeling of a series of widths cut from the web material, this being carried out with controlled winding tensions.