Adapter (3) for connecting a receptacle connector to a connection socket of a dialysis machine, the connector being provided with two fluid lines connecting the inside and outside of the receptacle, the ends of which, open towards the outside, are concentric, the connection socket of the dialysis machine being provided with two fluid lines, the ends of which, open towards the outside, are non-concentric and distant from each other. According to the invention, the adapter (3) is provided with 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 provided, while the second, placed around the first, forms an annular chamber open towards the outside, in the bottom of which a second orifice is provided, the adapter also being provided with a first connection channel (306) in which the first orifice coming from the first circular chamber opens out and a second connection channel (307) isolated from the first, in which the second orifice coming from the second annular chamber opens out, each channel (306, 307) comprising a connecting piece (308, 309) consisting of a circular tube, the said connecting pieces (308, 309) being sized and disposed so that they can be introduced into the reception elements of the coupling socket (2) of the dialysis machine.
