An air fuel ratio control system is so arranged to restrain a undesired variation of an air fuel ratio due to an on off control of a canister purge and thereby prevent deterioration of an exhaust performance. When a purge cut valve is closed to cut off the canister purge, the control system changes a feedback air fuel ratio corrective factor ALPHA like a step change to a predetermined initial value EVALP# to meet a leaning change of the air fuel ratio caused by the purge cut. When the purge cut valve is opened to resume the canister purge, the control system meets an enriching change of the air fuel ratio caused by restarting of the purge by producing a step change in the corrective factor ALPHA to an initial value EALPHA.times.KEVAL# determined in accordance with a value EALPHA of the corrective factor ALPHA obtained immediately before the cutoff (KEVAL# is a constant).