The internal combustion engine has at least two partly separate exhaust systems in each of which are disposed a catalytic converter, and upstream thereof, a lambda probe. There is provided a secondary air pump and a number of individual secondary air lines, corresponding to the number of exhaust systems, for delivering secondary air to the respective exhaust systems. From the signal of at least one air mass meter, a value is determined for the total air mass flow introduced into the exhaust systems. In order to determine the air mass actually introduced into the individual exhaust systems, the output signals from the lambda probes in the exhaust systems are used to identify an uneven distribution of the air mass fed to the individual exhaust systems.