The invention relates to home hemodialysis or peritoneal dialysis to be carried out by the patient or other non-professional users. The invention provides a system based on re-circulation of dialysate from small dialysate containers, which allows for very small dialysate consumption and easy portability. The system thereby also allows for long-duration dialysis without use of large volumes of dialysate. The invention may be implemented as a hemodialysis system, a process for administering dialysate, or as a method for performing dialysis.