A dialysis apparatus to be used for a device such as an artificial kidney. The apparatus is primarily formed by a single semipermeable membrane supported, as by wires, in such a way that it has a configuration defining two groups of tubes which can only communicate with each other through the membrane itself. Thus, the single membrane is supported by the wires and suitable tubular extensions to define two groups of tubes separated from each other only by the membrane itself so that the fluids to be treated can be subjected to diffusion, or osmosis through the membrane from one of the groups of tubes to the other of the groups of tubes while permitting collection of separated components to take place.