The invention is directed to a fuel-injection arrangement for a two-stroke engine in a portable handheld work apparatus such as a motor-driven chain saw or the like. Fuel is drawn by suction from a fuel tank by a fuel-feed pump and is made available at the suction connection of an injection pump. The injection pump has a pressure connection which is connected to an injection line through which the engine is supplied with fuel. A rapid start of a two-stroke engine provided with this fuel-injection arrangement is achieved by providing a bypass line which conducts fuel and bypasses the injection pump. A switchable flow valve is mounted in the bypass line. The bypass line opens directly into the intake channel conducting combustion air to the engine so that even without the pump action of the injection pump, adequate fuel is made available to the engine for starting the same.