A worm reduction gear, comprising: a housing which includes a guide holding portion; a worm wheel which includes a wheel tooth; a worm which includes a worm tooth meshing with the wheel tooth; a bearing which is externally fitted to a tip end portion of the worm; a holder member which includes a holder-side holding surface for internally fitting and holding the bearing and a holder-side held surface eccentric to a center axis (O 40) of the holder-side holding surface; a guide member including a guide-side holding surface for internally fitting and holding the holder member to be capable of swinging about a center axis (O 42) of the holder-side held surface, and is internally fitted and held into the guide holding portion; a first elastic urging member for elastically urging the tip end portion of the worm toward the worm wheel by elastically urging the holder member in a direction to rotate with respect to the guide member; wherein: an outer peripheral surface of the guide member has a cylindrical surface shape and is eccentric with respect to a center axis (O 48) of the guide-side holding surface; an eccentric direction of a center axis (O 42) of the holder-side held surface with respect to a center axis (O 40) of the holder-side holding surface and an eccentric direction of a center axis of an outer peripheral surface of the guide member with respect to a center axis (O 48) of the guide-side holding surface are opposite to each other; an amount of eccentricity of the center axis (O 42) of the holder-side held surface with respect to the center axis (O 40) of the holder-side holding surface and an amount of eccentricity of the center axis (O 50) of an outer peripheral surface of the guide member with respect to the center axis (O 48) of the guide-side holding surface are the same; characterized in that the first elastic urging member is disposed on the worm wheel side out of both axial side portions of the bearing. a housing which includes a guide holding portion; a worm wheel which includes a wheel tooth; a worm which includes a worm tooth meshing with the wheel tooth; a bearing which is externally fitted to a tip end portion of the worm; a holder member which includes a holder-side holding surface for internally fitting and holding the bearing and a holder-side held surface eccentric to a center axis (O 40) of the holder-side holding surface; a guide member including a guide-side holding surface for internally fitting and holding the holder member to be capable of swinging about a center axis (O 42) of the holder-side held surface, and is internally fitted and held into the guide holding portion; a first elastic urging member for elastically urging the tip end portion of the worm toward the worm wheel by elastically urging the holder member in a direction to rotate with respect to the guide member; wherein: an outer peripheral surface of the guide member has a cylindrical surface shape and is eccentric with respect to a center axis (O 48) of the guide-side holding surface; an eccentric direction of a center axis (O 42) of the holder-side held surface with respect to a center axis (O 40) of the holder-side holding surface and an eccentric direction of a center axis of an outer peripheral surface of the guide member with respect to a center axis (O 48) of the guide-side holding surface are opposite to each other; an amount of eccentricity of the center axis (O 42) of the holder-side held surface with respect to the center axis (O 40) of the holder-side holding surface and an amount of eccentricity of the center axis (O 50) of an outer peripheral surface of the guide member with respect to the center axis (O 48) of the guide-side holding surface are the same; an outer peripheral surface of the guide member has a cylindrical surface shape and is eccentric with respect to a center axis (O 48) of the guide-side holding surface; an eccentric direction of a center axis (O 42) of the holder-side held surface with respect to a center axis (O 40) of the holder-side holding surface and an eccentric direction of a center axis of an outer peripheral surface of the guide member with respect to a center axis (O 48) of the guide-side holding surface are opposite to each other; an amount of eccentricity of the center axis (O 42) of the holder-side held surface with respect to the center axis (O 40) of the holder-side holding surface and an amount of eccentricity of the center axis (O 50) of an outer peripheral surface of the guide member with respect to the center axis (O 48) of the guide-side holding surface are the same; characterized in that the first elastic urging member is disposed on the worm wheel side out of both axial side portions of the bearing.