A two-stroke engine (1) is especially for a handheld work apparatus such as a motor-driven chain saw, a cutoff machine or the like and has a cylinder (2) wherein a combustion chamber (3) is formed. The combustion chamber (3) is delimited by a reciprocating piston (5). The piston (5) drives a crankshaft (7) via a connecting rod (6). The crankshaft (7) is rotatably journalled in the crankcase (4). The combustion chamber (3) is connected to the crankcase (4) at pregiven piston positions via at least one transfer channel (11). The combustion chamber (3) has an outlet (10) for exhaust gases. An air channel (9) is provided which conducts combustion air into the crankcase (4) and a throttle element is mounted in the air channel (9). A compact configuration of the two-stroke engine (1) can be achieved when a separate fuel inlet (13) is provided in the crankcase (4) which is fed by a fuel metering system (15). The fuel metering system (15) has means for supplying fuel in dependence upon the position of the throttle element and/or in dependence upon the engine rpm. A method for operating the two-stroke engine (1) provides that the fuel is prepared to an air/fuel mixture in the crankcase (4) with the combustion air supplied via the air inlet (14).