Abstract: In a process for making a connection between superconductive wires constituted by one or more strands or filaments of superconductive material embedded in a metallic matrix, the metal constituting the matrix is previously eliminated over a certain length of wire, corresponding to the desired zone of contact between the wires, so as to expose the or each strand of these wires. Thereafter the linkage is established between the strands by exerting thereon a strong pressure, cold.The visible superconductive strands of the two wires are applied, near one another, on a support. A strip of superconductive material is then applied on the visible strands and a sheath made of a material which is a good conductor of electricity is placed around the assembly constituted by the support, the strands of the superconductive wires and the superconductive strip.