Abstract: The device applies to conducting cables with a metal protective shield of small thickness, inserted between the conductor or conductors of the cable and an insulating outer jacket. The device, providing, for example, the grounding of the shield, includes a connector having a rigid body capable of bearing on the periphery of the cable, and a flexible filiform conducting element provided for encircling the cable, the latter being positioned in a transverse groove progressively hollowed out, by mechanical and/or thermal effect, with the aid of a cord or other filiform flexible member, in the insulating outer jacket over at least a fraction of its circumference and reaching the shield. A mechanism is provided on the connector for immobilizing, and mechanically tensioning in a controlled manner, that part of the flexible conducting element encircling the cable.