In an apparatus for filtering and separating a flow medium by way of membranes disposed in a pressurized housing, which has an inlet for supplying the flow medium to the housing and outlets for discharging the retentate and the permeate from the housing, the membrane structure comprises a central permeate collection and discharge structure to which a plurality of membrane pillows are connected so as to extend therefrom in a spiral pattern and each membrane pillow is in communication with a permeate inlet opening in the permeate collection and discharge structure through which permeate is conducted out of the membrane pillow into the central permeate collection and discharge structure and to the retentate outlet.