A heat exchanger includes a bundle of tubes, which can be inserted into a tubular housing. Exhaust gas can flow through the tubes. A coolant duct can be arranged between the tubes. The bundle of tubes can have at least one grid-like securing structure which supports the bundle in the housing. The behavior of the heat exchanger with respect to vibrations is affected by outwardly curved metallic springs attached to the bundle of tubes which may be deformed in the opposite direction to the insertion direction of the bundle into the housing. The spring force is directed against the housing in order to dampen vibrations. The heat exchanger can also include an elastic device for permitting a change in length caused by temperature changes.