The invention relates to a dialysis apparatus comprising a dialyzer (4) that includes a cluster of capillary membranes (8), each of which has an outer face (13) and an inner face (14), the mean pore size being larger in the area of the outer face (13) than in the area of the inner face (14), further comprising a blood circulation system (6) and a dialysate circulation system (7), the blood circulation system (6) extending along the outer faces (13) and the dialysate circulation system (7) extending along the inner faces (14).
