In a winding machine, a plurality of yarns are wound on coaxial bobbins. The traversing device consists of two fliers rotating in the same direction for each winding region. The fliers of all the traversing regions are arranged in only two planes of rotation. The fliers of a plane of rotation overlap with their circles of rotation and have the same axial spacing from traversing region to traversing region, with a phase shift of 90 DEG .
