Abstract: The invention relates to a method of tightly electrically connecting an electric cable (12) to an end member (10) such as an electric contact, it is proposed that the partly bared or stripped end of the cable be introduced into a stepped blind hole (26) formed in a rear connection part (10b) of the member (10). More specifically, the bared cable end is received in two cylindrical sections (26a,26b) of the hole (26), in which have been inserted beforehand a transparent sleeve (30), capping an inspection hole (32), and a metal interface ring (34). The unbared part of the cable is received in a cylindrical entrance section (26c) of the hole (26). Then, by wiredrawing, the partly truncated cone-shaped, outer surface of the part (10b) is deformed in order to give it a cylindrical shape.