Abstract: A machine for winding, with a very short pitch, on a cable (1), at least one metal sheathing wire (5), comprising a first means for translatably moving a rectilinear portion of the cable in accordance with its axis and at least one coil (4) for distribution of said wire arranged on a coil-holder (3) subjected to turning around said cable in a perpendicular plane to said axis, with said wire passing on a grooved pulley (8) which is arranged between the coil and the cable and which has a fixed axis in relation to the coil, characterized in that the pulley (8) is provided with a driving means (9, 18, 20, 21, 22, 23) in rotation at an adjustable speed.