An electric power steering device having a resin gear used in a speed reduction gear mechanism and the resin gear used for the device are provided. The speed reduction gear mechanism includes a driven gear that is the resin gear integrally formed by fitting a resin part having gear teeth formed on the outer peripheral surface thereof to the outside of a metal core and a drive gear meshed with the driven gear. The resin part of the resin gear is formed of a resin composition having, as a base resin, a polyamide resin containing 10 to 50% by weight of glass fiber of 5 to 9 .mu.m in diameter, and has excellent wear resistance, durability, and dimensional stability. Grease on the meshed surfaces of the gears has such a composition that includes a thickener and 3 to 10% by weight of a wax having a melting point or softening point in the range of 70 to 130.degree. C. in a base oil formed mainly of at least one oil selected from mineral oil, poly .alpha.-olefin oil, and alkyl polyphenyl ether.
In an electric power steering system providing steering assist by applying a power of an electric motor to a steering mechanism via a reduction mechanism, the steering mechanism extending from a steering member to dirigible wheels, a grease (viscous material) is applied to a meshing engagement portion between teeth portions disposed on a motor-power transmission path extending from the electric motor to the steering mechanism via the reduction mechanism, the grease having a viscosity constant C satisfying 0.8 J.omega.p.ltoreq.C where J denotes the inertia of the electric motor, and cop denotes the resonant angular frequency of the steering mechanism including the electric motor and the reduction mechanism. This provides for the prevention of the occurrence of rattling noises caused by a vibration system including the reduction mechanism and the electric motor and the degradation of the steering feeling.