The invention relates to an adapter (3) for connecting a container connector to a connection socket of a dialysis machine. The container connector is provided with two fluid lines connecting the inside and the outside of the container, whereby the ends that open to the outside are concentric. The coupling socket of the dialysis machine is provided with two fluid lines, whereby the ends that open to the outside are not concentric and are spaced apart. According to the invention, the adapter (3) includes first (301) and second (302) concentric adapter ribs. The first rib forms a circular chamber open to the outside and the base of which is provided with a first opening, while the second rib surrounds the first and forms an annular chamber open to the outside and the base of which is provided with a second opening. In addition, the adapter is provided with a first linking channel (306) into which the first opening from the first circular chamber opens and a second linking channel (307) insulated from the first channel and into which the second opening from the second annular chamber opens. Each channel (306, 307) includes an end piece (308, 309) formed by a circular tube, said end pieces (308, 309) being sized and arranged so that they can be inserted into the receiving members of the connection socket of the dialysis machine.
