An air fuel ratio control apparatus for an internal combustion engine can achieve control behavior with good stability and response that is appropriate for a delay in an oxygen storage operation of a catalyst, and can always keep the state of purification of the catalyst adequately. The apparatus includes an upstream oxygen sensor (13), a downstream oxygen sensor (15), a first air fuel ratio feedback control section (130) that adjusts an amount of fuel to be supplied so as to make an air fuel ratio in an upstream exhaust gas and an upstream target air fuel ratio (AFobj) coincide with each other, and a second air fuel ratio feedback control section (150) that operates the upstream target air fuel ratio (AFobj) in accordance with an air fuel ratio deviation between an air fuel ratio detected by the downstream oxygen sensor (15) and a downstream target air fuel ratio so as to make the detected air fuel ratio of said downstream oxygen sensor (15) and the downstream target air fuel ratio coincide with each other. The second air fuel ratio feedback control section (150) sets an integral gain of integral calculation to be larger in accordance with an increasing flow rate of the exhaust gas, and also sets a proportional gain of proportional calculation so as not to be changed with respect to a change in the flow rate of the exhaust gas.