An electric power steering apparatus comprises a speed reduction mechanism for decelerating the rotation of an output shaft in an electric motor for steering assist. The speed reduction mechanism comprises a driving gear connected to the output shaft in the electric motor and a driven gear meshed with the driving gear. One of respective tooth sections in the driving gear and the driven gear includes a tooth section formed of a material having a relatively low hardness, and the other tooth section includes a tooth section formed of a material having a relatively high hardness. The profile of the tooth section formed of the material having a relatively low hardness is shifted in the direction in which the thickness at the root of the teeth of the tooth section is increased. The profile of the tooth section formed of the material having a relatively high hardness is shifted in the direction in which the thickness at the root of the teeth of the tooth section is decreased.