Abstract: In order to cut a paper web, which is wound in a drum reel-up, by means of a transverse strip forming a free wedge-shaped end, which is passed around a new reeling drum (7a) driven by a surface winding drum, the invention proposes an apparatus comprising a conveying channel (15) having a longitudinal aperture (19) facing the surface winding drum (4), and extending below the web (2) up to the vicinity of a nip (27) defined by the surface winding drum (4) and the new reeling drum (7a) at a place beside the web. The conveying channel (15) is provided with means for producing gas jets (44, 45) arranged to actuate from both sides a length of strip (29a) inserted into the conveying channel (15) in such a manner as to maintain it in position therein for conveyance to the nip (27).