Oxygenator (1; 101) for the gas exchange between blood and a gas in an extracorporeal lung support system, with - at least one oxygenator module (10; 110), with • several layers of semipermeable, gas-perfusable hollow fibers, with the hollow fibers of one of the layers being oriented at an angle of rotation about a central longitudinal axis of the oxygenator module (10; 110) with respect to the hollow fibers of another one of the layers; and • a potting, which extends along the central longitudinal axis and in which hollow fibers are fixed, wherein the potting defines a cavity that extends along the central longitudinal axis and in which hollow fibers are arranged and which is blood-perfusable in the direction of the central longitudinal axis, whereby the potting has an essentially circular inner sheath surface which limits the cavity radially outward; - a blood inlet (4.1) and a blood outlet (4.2), respectively coupled with a blood-perfusable cavity of the oxygenator module (10; 110); and - a housing (2; 102) to accommodate the oxygenator module (10; 110), wherein the housing (2; 102) has a gas inlet and a gas outlet, each of which is coupled to the hollow fibers of the oxygenator module, whereby the oxygenator has - a distributor device (30; 40; 45; 130) which is arranged, with respect to the central longitudinal axis of the oxygenator module (10; 110), upstream of the at least one oxygenator module (10; 110) and downstream of the blood inlet (4.1), wherein the oxygenator is set up for a central inflow of the oxygenator module, characterized in that the distributor device has a swirl distributor and is designed to guide a blood stream with a swirl at a flow angle to the central longitudinal axis into the cavity. - at least one oxygenator module (10; 110), with • several layers of semipermeable, gas-perfusable hollow fibers, with the hollow fibers of one of the layers being oriented at an angle of rotation about a central longitudinal axis of the oxygenator module (10; 110) with respect to the hollow fibers of another one of the layers; and • a potting, which extends along the central longitudinal axis and in which hollow fibers are fixed, wherein the potting defines a cavity that extends along the central longitudinal axis and in which hollow fibers are arranged and which is blood-perfusable in the direction of the central longitudinal axis, whereby the potting has an essentially circular inner sheath surface which limits the cavity radially outward; • several layers of semipermeable, gas-perfusable hollow fibers, with the hollow fibers of one of the layers being oriented at an angle of rotation about a central longitudinal axis of the oxygenator module (10; 110) with respect to the hollow fibers of another one of the layers; and • a potting, which extends along the central longitudinal axis and in which hollow fibers are fixed, wherein the potting defines a cavity that extends along the central longitudinal axis and in which hollow fibers are arranged and which is blood-perfusable in the direction of the central longitudinal axis, whereby the potting has an essentially circular inner sheath surface which limits the cavity radially outward; - a blood inlet (4.1) and a blood outlet (4.2), respectively coupled with a blood-perfusable cavity of the oxygenator module (10; 110); and - a housing (2; 102) to accommodate the oxygenator module (10; 110), wherein the housing (2; 102) has a gas inlet and a gas outlet, each of which is coupled to the hollow fibers of the oxygenator module, whereby the oxygenator has - a distributor device (30; 40; 45; 130) which is arranged, with respect to the central longitudinal axis of the oxygenator module (10; 110), upstream of the at least one oxygenator module (10; 110) and downstream of the blood inlet (4.1), wherein the oxygenator is set up for a central inflow of the oxygenator module, characterized in that the distributor device has a swirl distributor and is designed to guide a blood stream with a swirl at a flow angle to the central longitudinal axis into the cavity.