An internal combustion engine has at least one cylinder, with which an injection valve for metering fuel is associated and an exhaust system with an exhaust gas catalytic converter. A first exhaust gas probe is disposed upstream of or in the exhaust gas catalytic converter, and a second exhaust gas probe is downstream. A lambda controller determines a regulating variable as a function of the first probe and a control variable acting on a fuel mass to be metered using the injection valve. A trim regulator determines a regulating variable thereof as a function of the second probe and the first trim control variable thereof as a function of a P regulator component and the second trim control variable thereof as a function of an I regulator component. A function of a predetermined evaluation of the first trim control variable decides whether the second trim control variable is adapted.