exhaust gas catalytic converter the fuel air ratio is thus regulated as the purification effect of exhaust gas catalytic converters depends on the fuel air ratio and is also satisfactory only within a highly limited value range referred to as the catalytic converter window of the fuel air ratio for the different exhaust gas components comprising hydrocarbon nitrogen oxide and carbon monoxide however the regulating dynamics during the regulation of the fuel air ratio decline in proportion to the magnitude of the error to be eliminated with the result that the regulation of the fuel air ratio is usually combined with a pilot control the pilot control here predefines a fuel air ratio as a working point for the regulation of the fuel air ratio with the result that the regulator then only has to eliminate small errors and therefore has good regulating dynamics the adaptation of the fuel air ratio has here the function of setting the pilot control in such a way that as far as possible minimum errors have to be eliminated at the working point of the regulator in order to achieve regulating dynamics which are as good as possible the control unit 1 permits here either an additive or factorial or multiplicative adaptation of the fuel air ratio as a function of the operating state of the spark ignition engine the lean mode being disabled both during the additive adaptation mode and during the factorial adaptation mode in order to disable the lean mode for a factorial adaptation mode the control unit 1 has an evaluation unit 9 the structure of.