Abstract: The invention relates to a recuperative heat exchanger comprising an elongate rotationally symmetric body of ceramic material having radially outwardly extending, flow channels of slot like cross-section extending along the axis of the body. Alternate flow channels extend further toward the surface of the body and further toward the axis of the body, respectively. Inlet and outlet openings are provided for the flow channels about at the ends of the body. The invention also comprises a process for making such a heat exchanger, including extruding ceramic material through an extrusion nozzle with a free cross-section in which core bodies are shaped and positioned for generating the flow channels and inner and outer cover walls defining the flow channels. The invention further comprises the extrusion nozzle in which the process is performed.