an oxygenator module for gas exchange between blood and a gas in an extracorporeal lung support system , with several layers of semipermeable , gas - perfusable hollow fibers , wherein the hollow fibers of one of the layers are oriented at an angle of rotation about a central longitudinal axis of the oxygenator module with respect to the hollow fibers of another one of the layers , and with a potting which extends along the central longitudinal axis and in which the hollow fibers are fixed , wherein the potting defines a cavity that extends along the central longitudinal axis and in which the hollow fibers are arranged and which is blood - perfusable in the direction of the central longitudinal axis , wherein the potting has an essentially circular inner sheath surface that limits the cavity radially outward : as well as a method for producing the oxygenator module .