The present invention relates to a system (1) for supplying an air-fuel mixture to a two-stroke internal combustion engine (2), comprising a carburettor (3) having a throttle valve (4) and a choke valve (5). The system further has a transfer passage (6) between a crankcase (7) chamber and a combustion chamber (8) of said engine (2). A supply conduit for additional air (9) is having an air valve (10) for said additional air, and said supply conduit for additional air (9) is being adapted to discharge the additional air into the top portion of said transfer passage (6) during a portion of a cycle of said two-stroke internal combustion engine (2). Further the air valve (10) is controlled by the throttle valve (4) so as to affecting a air valve opening state when said throttle valve opening state is affected, and the opening state of said air valve (10) is delimited by a choked state of said choke valve (5) regardless of the throttle valve opening state.