Abstract: A motor-driven air pump operates when an engine is starting so that warming-up of an exhaust gas purifying catalyst may be expedited. The air pump has a low ventilation resistance to pass secondary air therethrough even when the pump is not driven by the motor. A high-response, low pressure-loss check valve is disposed in a passage connecting the catalyst in the exhaust gas passage and the air pump. When the engine is decelerating, the pump is not driven. However, the secondary air is introduced to the catalyst through the high-response, low pressure-loss check valve from the pump under the negative pressure caused by pulsation of the exhaust gas pressure. Thus, a bad smell from the catalyst may be prevented without increasing the size of the air pump and the motor.