A device is provided for connecting two hybrid electrical transmission cables each having stranded first conductive wires made of a first metal in the central zone of the cable and second conductive wires that are made of a second metal of higher hardness than that of the first metal and wound on and outside this central zone, the second conductive wires of the cables being connected by an external conductive sleeve. The central first wires of the cables are connected by a weld made of the first metal and connecting their end, this weld and this end being covered by a tube of metal of hardness equal to or higher than that of the second wires, at least partially in line with the sleeve, the end of the second wires being re-formed on the first wires and on the tube under the external conductive sleeve.