Abstract: The invention relates to a heat exchanger (10) having an elongate hollow body with connections (12, 12?, 13, 13?) for the supply and discharge of a first and of a second medium, in which the first medium is guided through the elongate hollow body in a counterflow with respect to a second medium, and the second medium flows through a spiral tube (11) which extends longitudinally axially between the end sides of the hollow body, and wherein a plurality of deflecting elements (18) projects into the hollow body interior from the hollow body inner casing, which deflecting elements deflect the flow of the first medium. To improve efficiency, it is provided that the deflecting elements project in an alternating sequence from in each case opposite hollow body sides into the hollow body interior and into the region of the spiral tube, in such a way that said deflecting elements end between two spirals, and that the hollow body inner casing has, in sections, a plurality of concavely-shaped constrictions.