NOVELTY - An apparatus (A1) for supporting a biofilm (B1) in a liquid comprises: (a) several gas permeable hollow fibers (F1), each having a lumen, an outer surface and an open end; and (b) a header having cavity and a port open to the cavity. (F1) Extend from the header, with outer surfaces of the open ends of the fibers sealed to the header and the lumens communicating with port through cavity.    USE - For supporting a biofilm in a liquid in the treatment of water e.g. wastewater (claimed).    ADVANTAGE - A hollow fiber gas transfer membrane and module supports biofilm and provides high gas transfer rate and adequate surface area for oxygen transfer at lower operating costs than the prior art processes. The hollow fiber membranes provide large surface area while avoiding the tendency of porous fibers to wet over time which results in a drastic drop in an oxygen transfer rates. The membrane and module exhibit high oxygen transfer efficiency. The module is built from fabric sheets with high packing density to permit good substrate velocities across the surface without recirculation of large volume of liquid.    DETAILED DESCRIPTION - An apparatus (A1) for supporting a biofilm (B1) in a liquid comprises:    (a) several gas permeable hollow fibers (F1), each having a lumen, an outer surface and an open end; and    (b) a header having cavity and a port open to the cavity.    (F1) Extend from the header, with outer surfaces of the open ends of the fibers sealed to the header and the lumens communicating with port through cavity. The fibers are made of melt spun thermoplastic polymer subjected to thermal or mechanical treatment after spinning to have at least an annular region of increased permeability to oxygen without permitting a flow of liquid water through the walls of the fibers from the outer surfaces to the lumens.    INDEPENDENT CLAIMS are also included for:    (1) a reactor comprising a tank for holding a liquid to be treated and having an inlet and outlet, (A1), and a gas delivery system for providing a gas to the port;    (2) treating a liquid involving:    (a) contacting (A1) or another apparatus (A2) having a port in communication with at least one inner surface of a gas permeable biofilm support medium (M1) with the liquid; and    (b) providing a gas to the port of the apparatus, the gas permeating to outer surfaces of (M1) to support a biofilm growing on the outer surfaces;    (3) cutting the ends of fibers in (A1) involving gluing a potting resin around the open looped ends of several fibers and then cutting through the resulting block of hardened resin and fibers;    (4) producing (A1) involving:    (a) adhering spacers to planar members parallel to but displaced from the open ends of (F1), first edge of the spacers is nearer to the ends of the fibers;    (b) inserting the planar members into a header cavity; and    (c) applying a potting resin over the second edge of the spacers extending from the planar members to walls of the header cavity; and    (5) process for supplying oxygen to a suspended growth bioreactor involving:    (a) immersing (A1) or (A2) having a port in communication with at least one inner surface of (M1) into the substrate of the suspended growth bioreactor; and    (b) providing oxygen bearing gas to the port, the oxygen travelling to the outer surfaces of the medium and into the substrate.