The invention relates to a device for placing sleeves on traveling articles, said sleeves being cut from a continuous sheath passing over a sheath-opening shaper, as far as and beyond cutter means, which shaper is held floating between first outer wheels and backing wheels carried by said shaper. In accordance with the invention, the alternating pivoting of the or each blade is ensured by means of a cam system by the difference in rotation between two superposed rotary rings constituting the support for said blade, one of the rings presenting a cam path parallel to the cutting plane and extending in an oblique direction, a cam sliding therein, which cam is constrained to pivot with a blade-carrier by means of a pin parallel to the common axis of the rings and pivotally mounted on the other ring, the or each blade being arranged to pierce the wall of the sheath and to cut said wall by exerting a force thereon that is directed radially outwards.