In an automobile engine exhaust gas cleaning system including an exhaust gas reactor which is supplied with auxiliary air for effecting combustion of unburnt constituents such as CO and HC in the exhaust gas, an air flow control device is provided for controlling the supply of the auxiliary air. The control device includes a first control valve disposed in the auxiliary air supply passage and controlled in response to the engine intake pressure so that it is opened when the engine intake vacuum is above the wide-open throttle vacuum, and a second control valve for controlling the supply of the engine intake vacuum to the first control valve in such a manner that it allows the engine intake vacuum to pass into the first control valve when the vacuum is lower than the value that is produced during deceleration and that it introduces atmospheric pressure to the first control valve when the vacuum increases to the value that is produced during deceleration. A time delay device is provided in the second control valve so that the atmospheric pressure to the first control valve is cut-off and the engine intake vacuum is again introduced into the first control valve after a certain time delay during initial period of engine deceleration.