Well-known are internal combustion engines which are provided with a three way catalyzer in their exhaust systems for reducing undesirable components, such as hydrocarbons (HC), carbon monoxide (CO) and nitrogen oxides (NO.sub.x), contained in exhaust gas. The above-mentioned three way catalyzer achieve their highest converting efficiency when the secondary air fuel ratio is suitably controlled so that it is maintained at the stoichiometric air fuel ratio. (The term "secondary air fuel ratio" as used herein is defined as the total amount of air, including secondary air, to the amount of the fuel fed into the engine.) Accordingly, many types of secondary air control devices have been proposed for maintaining the secondary air fuel ratio at the stoichiometric air fuel ratio. However, these proposed devices are intended to control the secondary air fuel ratio so that it coincides with the stoichiometric air fuel ratio at all times and are very complicated. Such complicated devices are difficult to adjust and maintain, and may be easily damaged. In addition, at least one part of such devices is always exposed to a high temperature caused by the exhaust gas and may also be thermally damaged thereby.
To eliminate the above-mentioned defects, the inventor of the present invention has conducted tests and confirmed that the alternate oscillation of the secondary air fuel ratio between the lean side and the rich side of the stoichiometric air fuel ratio can generate a higher converting efficiency of the three way catalyzer for reducing undesirable components, such as HC, CO and NO.sub.x, than maintaining the secondary air fuel ratio at the stoichiometric air fuel ratio.