The invention relates to a two-stroke engine in the form of a drive motor in a motor-driven chain saw or like portable handheld work apparatus. A combustion chamber (4) is provided in a cylinder (2) of the engine and is delimited by a piston (1). The piston (1) drives a crankshaft (6) via a connecting rod (5) and the crankshaft (6) includes a crankweb (7). The combustion chamber (4) is connected via an outlet to an exhaust-gas muffler. A fresh mixture is supplied to the combustion chamber (4) from the crankcase (3) via a transfer channel (10). The entry of the fresh mixture takes place via the crankcase (3). Also, an air channel (21) is provided for supplying fuel-free air. To reduce the scavenging losses, the air channel (21) is connected via a storage space (20) to the crankcase (3). The transfer channel (10) is either connected directly via a valve (23) to the crankcase or indirectly via the storage space (20).