In a blood dialysis system including a source of substitution fluid ( 10 ) and a blood dialysis machine, a hemodiafiltration system having a first dialyzer ( 1 ) including a first blood compartment ( 4 ) having a first blood inlet which receives blood to be cleaned and a first blood outlet which discharges partially diafiltered blood and a first dialysate compartment ( 5 ) having a first dialysate inlet and a first dialysate outlet, means ( 8 ) for mixing the partially diafiltered blood with substitution fluid from the source to obtain a blood/substitution fluid mixture, and a second hemofilter ( 2 ) including a second blood compartment ( 11 ) having a second blood inlet which receives the blood/substitution fluid mixture and a second blood outlet which discharges filtered blood and a second permeate compartment ( 12 ) having a second permeate outlet.
