Oxygenators (1) used for gas exchange are such that the pumped bloodflow is passed through a continuously moving blood-permeable exchange wall, the oxygenator having a number of specified features relating to the arrangement of and rotation means for a fiber bundle serving as the wall and also to the flow regime. An independent claim is also included for operation of the oxygenator by continuously rotating the wall (fiber bundle) and leading a fluid (especially blood) through the oxygenator.
