A first exhaust gas sensor signal (vls_up) of a first exhaust gas sensor (AS1) is detected. In addition, a second exhaust gas sensor signal (vls_down) of a second exhaust gas sensor (AS2) is detected. A relevant first estimated value of an emission of at least one exhaust gas component is determined in relation to a position of the first exhaust gas sensor (AS1) in the exhaust gas tract as a function of the first exhaust gas sensor signal (vls_up) and a relevant second estimated value of an emission of the at least one exhaust gas component is determined in relation to a position of the second exhaust gas sensor (AS2) in the exhaust gas tract as a function of the second exhaust gas sensor signal (vls_down). A conversion rate (K) of the at least one exhaust gas component is estimated as a function of a ratio of the second estimated value and the first estimated value of the determined emission. The exhaust gas catalytic converter is diagnosed as a function of the determined conversion rate (K).