In a hemodiafiltration apparatus, a membrane device (2) comprises a blood chamber (3) and a fluid chamber (4) separated by a semipermeable membrane (5). A grounding device (17) is connected to the discharge line by means of a tubular connector (16) made of an electrically-conductive plastic material. The grounding device can disconnect the grounding connection if the leakage current measured on a patient (1) connected to the apparatus exceeds a predetermined value. The apparatus can be classified as Cardiac Floating and, at the same time, causes no disturbances to an electrocardiograph connected to the patient.