A heat exchanger (7) for an exhaust system (5) of an internal combustion engine (1), includes a heating tube (16) for carrying hot exhaust gas and a cooling tube (17) for carrying a liquid cooling agent. A thermoelectric generator (13) generates an electric voltage from a temperature difference and is arranged with the adjacent tubes in a stacking direction (18) to form a stack (21). A support tube (28) is supported in the stacking direction on wall sections (29) of the respective tube (16, 17), which wall sections mutually face each other, and is arranged in the respective heating tube (16) and/or cooling tube (17). Increased energy efficiency is achieved if at least two support tubes (28), which differ from one another by tube length and/or tube end (30) and/or by tube cross sections, are arranged in the respective tube (16, 17) at right angles to a longitudinal direction (31).