A handheld work apparatus has a fan wheel and a combustion engine having a cylinder and a crankcase. The fan wheel, arranged in a housing, is driven by the engine in a rotational direction. The housing includes a rear wall and a peripheral delimiter having a first and a second end delimiting an outlet for cooling air for the cylinder. The outlet extends from the second to the first end in the rotational direction. A throughflow-opening is provided in the housing, through which the cooling air flows out to the outside of the crankcase. The angular distance, measured proceeding from the first end in the rotational direction, between the first end and the throughflow-opening is smaller than the angular distance, measured proceeding from the throughflow-opening in the rotational direction, between the throughflow-opening and the second end. The angular distances are each measured about the rotational axis as a peripheral angle.