A device (1) for fastening elongate elements (2) such as cables or bundles of cables or the like to a structure (S) includes at least a first flexible self-gripping strip (3) having a loop-closure system on a first face (30) and a second flexible selfgripping strip (4) with a hookclosure system on a first face (40) The first and second flexible strips (3 and 4) adhere at least in par.t one against the other via their second faces (35 and 45) that are self-adhesive, so as to form a flexible collar (C) by uniting at least their facing free end zones (51 and 52) The device further includes a rigid plate (10) for constituting a support for fastening the device (1) to the structure (S).