An internal combustion engine has an exhaust gas aftertreatment system comprising in the given order in the flow direction of the exhaust gas: a device for metering ammonia and/or a compound that can be decomposed to form ammonia into the exhaust gas to be cleaned, as a reducing agent; one or more SCR catalysts, which form a first SCR unit; one or more SCR and/or ammonia oxidation and/or ammonia slip catalysts, which form a second SCR unit; and a NOx sensor in the exhaust gas tail pipe. An amount, to be metered into the exhaust gas, of ammonia and/or of the decomposable compound is set using the nitrogen oxide concentration in the exhaust gas tail pipe that is determined by the NOx sensor, and the occurrence or non-occurrence of an ammonia excess in the region of the NOx sensor can be determined from the sensor signal of the NOx sensor by evaluating said sensor signal.