The invention relates to a fuel-metering arrangement for the mixture-forming unit (2) of an internal combustion engine (10) in a portable handheld work apparatus. The mixture-forming unit comprises a fuel store (30), a switchable valve (40) and a fuel channel (20) which opens into an intake region of the engine (10). The valve (40) has an inflow port (41) which is connected to the fuel store (30) and an outflow port (42) which is connected to the fuel channel (20). A fuel column is mechanically moved by the switching of the valve. In order to compensate for this fuel column, the outflow port (42) is connected via a bypass channel (45) to the inflow port (41) and a flow valve (46) is mounted in the bypass channel (45). The flow valve (46) opens in flow direction (48) from the outflow port (42) to the inflow port (41) and blocks in the direction opposite thereto.