Adapter (3) for connecting a receptacle connector to a connection socket of a dialysis machine, each provided with two fluid lines, whose ends are concentric on the connector and non-concentric and distant from each other on the socket. The adapter (3) has concentric first (301) and second (302) adapter ribs, the first forming a circular chamber open towards the outside, in the bottom of which a first orifice is produced, while the second forms an annular chamber open towards the outside, in the bottom of which a second orifice is produced. The adapter also has first and second connection channels (306, 307) isolated from each other, in which the first and second orifices coming from the first and second annular chambers open out. Each channel (306, 307) includes a connecting piece (308, 309) consisting of a circular tube, for introduction into the reception elements of the coupling socket (2).
