Air-fuel ratio control apparatus for internal combustion engine

The characteristics of an output of an exhaust gas sensor with respect to the air-fuel ratio of an engine (1) are expressed by a nonlinear function such as a quadratic function or the like, and the parameters of the nonlinear function are sequentially identified according to a sequential identifying algorithm using data of the output of the exhaust gas sensor (5) and the data of the output of an air-fuel sensor (4) which detects the air-fuel ratio of the engine. An air-fuel ratio at which the function value of the nonlinear function whose parameters have been identified is used as a target air-fuel ratio, and the air-fuel ratio of the engine is controlled at the target air-fuel ratio.