order lag accordingly calculator 18 makes the calculation of a first order lag dependent on engine speed n and air flow q the section 20 operates to gradually change the output corrected ratio of the section 19 in accordance with the first order lag from the calculator 18 by a proper method for example by weight means thus the desired ratio from the table 11 is corrected with transport time delay and response delay the corrected ratio afdc is applied to an adder 15 on the other hand the desired air fuel ratio afd is applied to an air fuel ratio coefficient k af and miscellaneous coefficient coef calculator 12 which produces a coefficient k af and a coefficient coef the adder 15 produces an error signal dependent on the difference between the corrected desired air fuel ratio afdc and the actual air fuel ratio afa calculated from the feedback signal from the lean mixture sensor 5 the error signal is applied to a feedback coefficient calculator 16 which produces a feedback coefficient k fb the coefficient k af coef and k fb are multiplied at a multiplier 13 and the product is applied to a fuel injection time calculator 14 where the above described calculation ti equation 1 is made to produce a fuel injection signal the fuel injection signal is applied to an engine e to inject fuel during the time ti fig4 shows the operation of the system from a step 101 to a step 110 the above described operations.