Factors affecting the response time of a transfer system from the combustion of injected fuel to the detection of its oxygen concentration include a stroke delay time due to an engine speed, the dependence of an LAF sensor response time on an exhaust gas flow rate, a response time change of the LAF sensor due to its deterioration with time, and the like. If a hyperplane of the sliding mode is fixed without considering the above-mentioned factors affecting the response time of the transfer system, an overshoot or oscillation of a feedback system may occur at low speeds of the engine even if preferable feedback responsiveness can be achieved, for example, at high speeds of the engine. This results in aggravated exhaust emissions, degraded drivability due to torque fluctuations, and fluctuations in idle speed.A hyperplane used in a control system for providing feedback control of an air-fuel ratio through sliding mode control is varied based on the factors affecting the response time of the control system within a range in which the control system can be stabilized.