An electric power steering apparatus having a compact and inexpensive backlash mechanism is provided by arranging its structure to easily adjust the backlash of the bevel gear mechanism, and at the same time, to pre-press the bearings so that the movement of the shaft in the axial direction can be regulated. The rotational shaft having a small gear coupled thereto which constitutes a bevel gear mechanism on one side is rotatively supported by a housing, but disabled to shift in the axial direction. The large gear which constitutes the bevel gear mechanism on the other side is coupled to the output shaft of a steering system so that it can shift in the rotational direction and axial direction together with the shaft. The output shaft is rotatively supported by bearings with respect to the housing with a movable sleeve which abuts upon the outer ring of the bearing. The movable sleeve can be driven in from the outside by means of an adjustment screw so that the backlash between the small and large gears can be adjusted, while the inner ring of the bearing can be driven in with respect to the output shaft by means of a lock nut to tighten the bearing which abuts upon the outer ring of the output shaft. In this way, the inner rings of the bearings are pressed inwardly themselves, hence removing the play thereof.