An internal combustion engine has a plurality of cylinders with fuel-metering injection valves, and an exhaust gas probe that generates a measurement signal characteristic of the air/fuel ratio in the respective cylinder. A correction signal for fuel mass to be metered is determined using a lambda controller as a function of the exhaust gas probe measurement signal. When at least one predefined condition is met within a predefined operating range of the engine, a cylinder-specific diagnosis relating to the emissions of pollutants is performed on the basis of unsmooth running, wherein the cylinder-specific diagnosis is actively performed only in a respective detection phase that is applied to a neutral value by a modified proportional discrete level of the correction signal and is performed with a modified integral parameter of the lambda controller that is reduced as compared with an integral parameter in a normal operating mode of the lambda controller.