Abstract: Proposed is a device for metering fuel into the exhaust system of an internal combustion engine. An injection valve is arranged in the exhaust system and is cooled by a flowing cooling liquid even in its closed state. The injection valve is supplied with fuel via a fuel inflow, from which a first partial flow is injected into the exhaust gas and from which a second partial flow is recirculated via a fuel collecting return line into a fuel storage tank. The fuel inflow is fed from a low-pressure system of an injection system which serves for metering fuel for combustions which take place in a combustion chamber of the internal combustion engine. The device has a damping mechanism, which is hydraulically connected to the fuel inflow, for damping pressure oscillations.