An exhaust gas heat exchanger comprises connection points for the exhaust gas flow, for connecting the exhaust gas heat exchanger to an exhaust gas supply line for supplying a hot exhaust gas and an exhaust gas withdrawal line for withdrawing the exhaust gas flow cooled in the exhaust gas heat exchanger. The exhaust gas flow flows through the exhaust gas heat exchanger in a bundle of exhaust gas guiding pipes in a flow direction. The exhaust gas heat exchanger is provided with at least one coolant supply connection and at least one coolant withdrawal connection. Coolant is guided in a coolant channel in the exhaust gas heat exchanger, inside which it flows around the bundle of exhaust gas guiding pipes. The coolant channel comprises at least two regions which differ in terms of the flow direction of the exhaust gas flow by divergent flow directions of the coolant.