A curling device for a filter tip attachment comprises at least one blade-like element offered to a continuous strip of paper material at a selected contact zone in such a way as to deform the material as it advances, so that single tipping papers separated from the strip by a cutting unit of the attachment are given a curved profile and as a result more easily wrapped around and affixed to the assembled filters and cigarette sticks when these are joined together; the curling device also comprises a delivery system by which the contact zone is flooded with a cushioning fluid designed to favor a smooth sliding contact between the curling element and the running strip, and at the same time equalize the tensions in the strip preceding and following the contact zone.