An electric power steering apparatus in which steering assistance is achieved by transmitting a rotary motion of an electric motor for steering assistance to a steering shaft on which a worm wheel is mounted through a worm shaft on which a worm is mounted, wherein the worm shaft is deflectable toward the worm wheel and equipped with a biasing member biasing the worm shaft in the deflective direction thereof, or alternatively, the worm wheel is deflectable toward the worm shaft and equipped with a biasing member biasing the worm wheel in the deflective direction thereof.