Abstract: To provide properly layered windings on a rotating spool, for example on a flanged spool carrier, the material is guided towards the spool at a predetermined angle of attitude, so that the windings on the spool body fall adjacent each other; the traverse of the spool with respect to the material supply position is so controlled, by means of an electronic control system, considering the width of the spool, the thickness of the material and winding speed, that the material will be wound on the spool pressed against the next previously applied winding and, at the end layers, the relative traverse speed (for example by axial shift of the winding spindle) is so controlled that, just before and after the formation of superimposed windings, the attitude angle of the supplied material will tend to become zero and then, after formation of a new winding layer, the attitude angle will reach the predetermined value.