This paper investigated highly precise control of the air fuel ratio (AFR) of a gasoline engine in a transient state acceleration or deceleration at several starting engine speeds and several intake valve opening (IVO) timings.First, a two-input and one-output linearized engine model was developed for the design of the AFR control system. In order to compensate for the AFR deterioration caused by the actuation of the throttle valve during acceleration or deceleration, a feed-forward (FF) controller was developed based on the model. In order to add adaptability to the FF controller, a compensation using an error value from the AFR target value was equipped. The feedback (FB) system was designed using a backstepping method that is well known as an adaptive controller for a non-linear system. By repeating several times of acceleration and deceleration, the FF and the FB controller performed in harmony as if those were fused in one controller, then, a precise AFR control results were obtained.Two sets of parameters in each controller were provided and an investigation was carried out as to which combination is superior for robustness regarding several initial starting engine speeds and IVO timings. The pressure and the flow rate of the internal EGR were altered momentarily according to the intake valve angle; therefore, large system parameter changes were recognized. By combining a fast response adaptive FF controller and a bit more moderate response backstepping FB controller, precise and robust AFR control results were attained.