An electric power steering apparatus comprising a rack shaft having two racks, a first rack-and-pinion mechanism for transferring a steering torque to the rack shaft, and a second rack-and-pinion mechanism for transferring an assist torque to the rack shaft. The second rack-and-pinion mechanism includes a pinion and a rack both being helical gears so that a large torque can be transmitted to the rack shaft. Teeth of the pinion and rack are arc profiled. The arc profiled teeth mesh with each other through a large contact area of concave and convex surfaces thereof and hence with a reduced contact pressure compared to involute profiled teeth. The arc profiled teeth thus have increased surface fatigue strength, bending strength and bending fatigue strength and can transmit an assist torque sufficiently to the rack shaft. Moreover, they have durability sufficient to withstand a torque load of a motor inertia.