A six-cycle engine has the advantage for the capability of internal cooling with scavenging air. This advantage enables the compressive ratio to rise, thereby achieving lower fuel consumption. However, there has been a critical problem due to lowered temperature of the exhaust catalyst and excessive volume of oxygen contained therein caused by the mixing of the scavenging air with exhaust gas. To solve the problem of lowered temperature, the invention has thermally insulated the fuel combustion chamber and the exhausting system, and controlled the aperture degree of the scavenging port valve relatively to the suction valve to adjust the scavenging air volume against the suction air, thereby controlling temperature of the exhaust gas. Further, to solve the problem of excessive volume of oxygen, the invention has introduced an EGR (Exhaust Gas Recirculation) system to fully substitute the scavenging air with circulating exhaust gas and a self EGR system to open the exhaust valve during the scavenging air introduction stroke. The present invention has successfully made a naturally good fuel-efficient six-cycle internal combustion engine be suited one for practical use such as conventional vehicles.