Abstract: Apparatus for processing fluids, in particular blood, includes a housing having an fluid inlet port and a fluid outlet port, with the housing being formed by an outer tube, an intermediate tube set within the outer tube for forming a first chamber therebetween, and an inner tube set within the intermediate for forming a second chamber therebetween. Disposed within the chambers are a plurality of hollow fiber membranes for suitably conducting heat exchange fluid and gas. The first and second chambers are so interconnected to one another and the inlet port and outlet ports are so disposed as to effect a fluid flow path through the chambers in longitudinal direction of the tubes.