A two-stroke cycle engine for introducing a air/fuel mixture and an air from a scavenging passage into a combustion chamber includes a valve body for adjusting the opening of an air supply passage, through which the air is supplied to the scavenging passage, and a second opening of a air/fuel mixture supply passage, through which the air/fuel mixture is supplied to the scavenging passage, a check valve for preventing the air within the air supply passage from flowing in a reverse direction, and a delay member projecting into the air supply passage on an upstream side of the check valve for delaying the timing at which the air reaches from the valve body to the air scavenging passage.