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The second-generation air-fuel ratio control method has been developed to reduce exhaust gas emissions in accordance with the improvements in catalysts. The control system consists of a feedforward control using a fuel behavior model, a feedback control using an universal exhaust gas oxygen (UEGO) sensor and a feedback control utilizing the heated exhaust gas oxygen (HEGO) sensor. This significantly improves air-fuel ratio tracking performance by feedforward control derived from the models that express the dynamic phenomena and the disturbance attenuation by UEGO feedback controller which compensates for the long dead-time characteristics by the state predictive control. The tracking performance and the disturbance attenuation can be achieved independently by a two-degree-of-freedom structure presented in this paper. The exhaust air-fuel ratio downstream of the catalyst precisely converges to stoichiometry, which maximizes the conversion efficiency of the catalyst.