A two-stroke engine includes a cylinder having a combustion chamber. The combustion chamber is delimited by a piston guided in a reciprocating manner in the cylinder and drives a crankshaft. A first intake channel opens into the crankcase interior. A transfer channel opens into the crankcase interior via a transfer window on a cylinder bore of the cylinder and via a passage opening. A second intake channel is provided for supplying scavenging air to the transfer channel. The first intake channel and the second intake channel are configured for supplying air. An injection valve configured for injecting the entire quantity of fuel to be supplied to the engine directly into the crankcase interior is disposed on the crankcase. A method for operating a two-stroke engine provides that the entire quantity of fuel to be supplied to the engine via a metering installation is supplied directly to the crankcase interior.