The invention relates to a two-stroke engine having an overflow channel through which an air/fuel mixture is supplied. The overflow channel is provided with a vaporization chamber having a hot wall against which fuel is injected and vaporized. The vaporized fuel is stored in the vaporization chamber and is carried into the combustion chamber of the engine by fresh air flowing in from the crankcase when the overflow channel is opened. Even at high rotational speed, a good mixture preparation is asssured.