Abstract: An apparatus and process for substance-specific treatment of fluids using groups of first and second treatment elements, adjacently positioned in a housing and made from membranes, the treatment elements having cavities open on one side, whereby the cavities of the first treatment elements are open in the direction of the inlet arrangement of the housing and the cavities of the second treatment elements are open in the direction of its outlet arrangement. A stream of the fluid to be treated is introduced via the inlet arrangement into a distribution space, which is delimited only by the housing, the inlet arrangement, and the ends, pointing to the inlet arrangement of the treatment element group adjacent to the inlet arrangement, and entering the cavities of the first treatment elements. The stream then flows successively through the walls of the first and second treatment elements, whereby the substance-specific treatment of the fluid takes place.