A dialysis machine making it possible to treat a body fluid, such as blood or plasma, said machine comprising: · a dialyzer including an enclosure housing a dialysis membrane that subdivides the enclosure into a compartment for passing said body fluid and referred to as the "body fluid compartment", and a compartment for passing dialysate and referred to as a "dialysate compartment"; said body fluid compartment having a body fluid inlet and a body fluid outlet, and said dialysate compartment having a dialysate inlet and a dialysate outlet; · a dialysate feed system comprising a dialysate feed line connected to the inlet of the dialysate compartment; and · a dialysate discharge system comprising a dialysate discharge line connected to the outlet of the dialysate compartment; · a control unit, such as a programmable controller, that comprises: · ultrafiltration control means making it possible to cause an aqueous quantity of the body fluid to pass through a portion of the membrane from the body fluid compartment into the dialysate compartment; and · back-filtration control means making it possible to cause the dialysate to pass through at least a portion of the membrane, from the dialysate compartment into the body fluid compartment; said dialysis machine being characterized in that the dialysate feed line is provided with a flow constriction, and said machine further comprises means for measuring the pressure difference (523, 524) across the terminals of said flow constriction; in that said dialysate feed system further comprises: - at least one flexible bag, referred to as a "ventricle bag", designed to contain the dialysate and connected to said feed line upstream from said flow constriction, said ventricle bag being contained in an enclosure; and - pressurizer means for putting the ventricle bag under pressure by pressurizing said enclosure; and in that said machine further comprises an open/close system (C5, C5') for opening/closing the dialysate discharge line, which system, when in the open state, allows the dialysate present at the outlet of the dialysate compartment to flow through said discharge line, and, when in the closed state, prevents the dialysate present at the outlet of said dialysate compartment from flowing through said discharge line. said back-filtration control means being configured to: - control said open/close system (C5, C5') so as to close the discharge line; and - when said discharge line is in the closed state, control the pressure applied to said ventricle bag as a function of the pressure difference measured across the terminals of the constriction, so as to obtain a given flow rate of dialysate. · a dialyzer including an enclosure housing a dialysis membrane that subdivides the enclosure into a compartment for passing said body fluid and referred to as the "body fluid compartment", and a compartment for passing dialysate and referred to as a "dialysate compartment"; said body fluid compartment having a body fluid inlet and a body fluid outlet, and said dialysate compartment having a dialysate inlet and a dialysate outlet; · a dialysate feed system comprising a dialysate feed line connected to the inlet of the dialysate compartment; and · a dialysate discharge system comprising a dialysate discharge line connected to the outlet of the dialysate compartment; · a control unit, such as a programmable controller, that comprises: · ultrafiltration control means making it possible to cause an aqueous quantity of the body fluid to pass through a portion of the membrane from the body fluid compartment into the dialysate compartment; and · back-filtration control means making it possible to cause the dialysate to pass through at least a portion of the membrane, from the dialysate compartment into the body fluid compartment; · ultrafiltration control means making it possible to cause an aqueous quantity of the body fluid to pass through a portion of the membrane from the body fluid compartment into the dialysate compartment; and · back-filtration control means making it possible to cause the dialysate to pass through at least a portion of the membrane, from the dialysate compartment into the body fluid compartment; - at least one flexible bag, referred to as a "ventricle bag", designed to contain the dialysate and connected to said feed line upstream from said flow constriction, said ventricle bag being contained in an enclosure; and - pressurizer means for putting the ventricle bag under pressure by pressurizing said enclosure; - control said open/close system (C5, C5') so as to close the discharge line; and - when said discharge line is in the closed state, control the pressure applied to said ventricle bag as a function of the pressure difference measured across the terminals of the constriction, so as to obtain a given flow rate of dialysate.