Artificial kidney for gradual, and at least semi-continuous, blood treatment, wherein a blood stream is fed from a body of a living human or animal being into the artificial kidney, where anticoagulation is first effected, blood cells and molecules of large and medium molecular weight, such as proteins, are then primarily separated from plasma and fed back to the blood stream, regulating a water and salt balance by diverting excess plasma water and further removing from the blood stream, plasma or plasma water accumulated and toxic substances, by removal of specific electrolytes and waste products and wherein purified or partially purified plasma and plasma water is being carried back to the blood tract of the body.