Adapter (3) for connecting a container connector to a socket connection of a dialysis machine, the connector being equipped with two fluid lines connecting the inside and the outside of the container whose open outward ends are concentric, the connection socket of the dialysis machine being provided with two fluid lines whose open ends towards outside are non-concentric and distant from each other. Consistent to the invention, the adapter (3) is provided with a first (301) and a second concentric adapter rib (302), the first forming an open circular chamber outwards in the bottom of which is made a first orifice while the second, placed around the first, forms an annular chamber open to the outside in the bottom of which is realized a second orifice, the adapter being furthermore provided with a first link channel (306) into which the first orifice coming from the first circular chamber and a second connecting channel (307) isolated from the first one into which the second port from the second annular chamber, each channel (306, 307) comprising a mouthpiece (308, 309) consisting of a circular pipe, said end pieces (308, 309) being dimensioned and arranged so that they can be introduced into the receiving elements of the taking of fitting of the dialysis machine.Adaptateur (3) pour raccorder un connecteur de récipient à une prise deraccord d'une machine de dialyse, le connecteur étantmuni de deux lignes de fluide reliant l'intérieur et l'extérieur du récipientdont les extrémités ouvertes vers l'extérieur sontconcentriques, la prise de raccord de la machine de dialyse étant munie dedeux lignes de fluide dont les extrémités ouvertes versl'extérieur sont non concentriques et éloignées l'une de l'autre. Conformémentà l'invention, l'adaptateur (3) est muni d'unepremière (301 ) et d'une seconde nervure d'adaptateur (302) concentriques, lapremière formant une chambre circulaire ouvertevers l'extérieur dans le fond de laquelle est réalisé un pre
