exemplary embodiment of a sheathed rope 20 according to the invention with regard to function and construction a rope core 21 and an intersheath 22 that is firmly bonded to it correspond to relative parts of the first exemplary embodiment described above a covering layer 23 of seventeen aramide fiber strands 24 is laid onto the intersheath 22 each individual aramide fiber strand 24 is given a separate seamless jacket 25 of polyurethane the aramide fiber rope 20 described so far is surrounded by a rope sheath 26 the rope sheath 26 as also the jacket 25 surrounding the aramide strands 24 consists of thermoplastically formable polyurethane and this material is welded in one piece to the covering layer of strands 23 along the corresponding external surface of the jacket 25 via these permanent molecular bonds the rope sheath 26 is bonded with positive fit to the aramide fiber rope 20 in this exemplary embodiment too anchoring means in the form of the jacket 25 are first anchored in the rope structure with positive fit and immediately prior to extrusion of the rope sheath 26 are permanently bonded to the rope sheath 26 by heating bonding with adhesive lightly corroding or vulcanizing in fig3 an aramide fiber rope 30 is shown as a third exemplary embodiment of the invention a rope core structure 31 an intersheath 32 surrounding it and a number of strands 33 of a covering layer of strands 34 are again.