The cable core wrapping device allows an elongate cord or web (FG) to be wound around the outside of the cable core (KS) with a given tension, using a measuring sensor (MF) in the path of the elongate cord or web fed off a supply reel (VS). An elastic element (BF), e.g. a spring blade, is inserted in the path of the elongate cord or web and is deflected in the axial direction of the rotation axis of the winding device (KO), for compensating short-term tension variations.