Dialysis apparatus including:structure (14) for preparing a dialysis liquid containing sodium, comprising structure (18) for regulating the sodium concentration;a dialysis liquid circuit comprising a feed line (12) and a discharge line (13), the feed line (12) having one end connected to the structure (14) for preparing dialysis liquid, and another end which can be connected to a dialyser (1), the discharge line (13) having an end which can be connected to the dialyser (1);structure (9, 10, 12) for infusing a patient with an infusion solution containing sodium and a substance A at determined concentrations [Na.sup.+ ]sol and [A]sol;structure (32) for determining the sodium concentration [Na.sup.+ ]dial of the dialysis liquid so that the patient's body tends towards a desired sodium concentration [Na.sup.+ ]des, as a function of the dialysance D of the dialyser (1) for sodium, of the desired sodium concentration [Na.sup.+ ]des inside the patient's body, of the infusion flow rate Qinf, and of the sodium concentration [Na.sup.+ ]sol of the infusion solution;control structure (32) for driving the structure (18) for regulating the sodium concentration of the dialysis liquid such that this concentration is equal to the determined concentration [Na.sup.+ ]dial.