Disclosed herein is an engine system which comprises an internal combustion engine, an air admission system to admit scavenging air, under pressure, into an engine cylinder through an additional intake valve and an EGR system. The air admission system includes an air pump and an EGR conduit of the EGR system having an inlet end connected to the engine exhaust conduit and an outlet end connected to the air admission system upstream of the air pump to effect admission of recirculated exhaust gas through the additional intake valve together with scavenging air. With this EGR system and the replacement of residual gas with scavenging air, the rate of exhaust gas in the engine cylinder upon ignition is kept substantially constant over varying partial loads.