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, first outer wheels serving to advance the sheath along the shaper, and second outer wheels being provided downstream from cutter means for the purpose of ejecting the cut-off sheath segment, said wheels being driven in rotation by associated electric motors controlled synchronously by a virtual-shaft common electronic programmer. In accordance with the invention, the programmer is arranged to determine a continuous profile of speed variation for the associated electric motors, said profiles being bell-shaped and having a common end segment in which the profiles coincide, this corresponding to the motors having identical speeds, the length of the common end segment being selected so that the sheath is advanced beyond the point of tangential contact with the second wheels so that said sheath is pinched by said second wheels prior to being held stationary for the cutting and ejection pass.