An additional air supply system for adjusting the air-fuel ratio of a mixture includes the improved control unit for actuating, at two different speeds, a drive motor of a bypass valve disposed in an additional air supply path. The control unit is provided with an air-fuel ratio discriminating circuit for generating high and low level signals by comparing a detected air-fuel ratio with the stoichiometric ratio, and an actuating circuit for producing pulse signals at each instant of inversion of the signal levels of the air-fuel ratio discriminating circuit in such that for a predetermined period from the instant of inversion a high frequency pulse signal is produced and then a low frequency pulse signal is produced for the remaining period until the next inversion. Since the pusle signals having two different frequencies are applied to the drive motor of the bypass valve, the bypass valve is drived at a fast speed to a predetermined amount of opening or closing and then moved slowly until the next inversion of the signal level.