A method is provided for operating a bivalent internal combustion engine, which may run lean with using a fuel with wide inflammability limits, such as hydrogen, whereby a first lean region close to the stoichiometric air ratio and a second lean region, adjacent to the first in the direction of greater .lamda. valve are defined. The operation in the first lean region is skipped such that operation occurs either in the second lean region or at an approximately stoichiometric air ratio.