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A fuel control method to reduce the harmful exhaust gas from SI engines is proposed. As is well known, both the amplitude and the frequency of the limit cycle in a conventional air-fuel ratio control system are determined uniquely by parameters in the system. And this limits our making full use of the oxygen storage effect of TWC. A simple model of TWC reaction revealed the relationship between maximum conversion efficiency and both the amplitude and the frequency in a air fuel control system. It also revealed that TWC conversion efficiency attained to maximum levels when both the amplitude and the frequency of the limit cycle are selected so as to make full use of the oxygen storage effect of TWC. In order to achieve this, it is necessary to vary both the amplitude and the frequency arbitrarily.