A worm reduction gear, comprising: a housing (12a, 12b) including a holding recessed part on an inner circumferential surface; a worm wheel including wheel teeth on an outer circumferential surface; a worm including worm teeth meshed with the wheel teeth on an outer circumferential surface; a bearing (18a, 18b, 18c) externally fitted to a tip part of the worm; and an inner diameter side holder (25, 25a, 25b, 25c) including a bearing holding part in which the bearing (18a, 18b, 18c) is internally fitted and held; characterized in that, the worm reduction gear further comprises: an outer diameter side holder (26, 26a, 26b, 26c, 26d, 26e) internally fitted and held in the holding recessed part, including a holder holding part (38a, 38b) in which the inner diameter side holder (26, 26a, 26b, 26c, 26d, 26e) is internally fitted and held so as to be able to be relatively rotated and moved and to be displaced in a direction orthogonal to a center axis of the worm wheel and a center axis of the worm; and an elastic urging member (28, 28a, 28b, 28c) in a circumferential direction elastically urging the inner diameter side holder (25, 25a, 25b, 25c) against the outer diameter side holder (26, 26a, 26b, 26c, 26d, 26e) in a direction of rotating in the circumferential direction, wherein when the inner diameter side holder (25, 25a, 25b, 25c) rotates in the circumferential direction with respect to the outer diameter side holder (26, 26a, 26b, 26c, 26d, 26e), an outer circumferential surface of the inner diameter side holder (25, 25a, 25b, 25c) and an inner circumferential surface of the outer diameter side holder (26, 26a, 26b, 26c, 26d, 26e) are formed so that the bearing (18a, 18b, 18c) is displaced in the direction orthogonal to the center axis of the worm wheel and the center axis of the worm. a housing (12a, 12b) including a holding recessed part on an inner circumferential surface; a worm wheel including wheel teeth on an outer circumferential surface; a worm including worm teeth meshed with the wheel teeth on an outer circumferential surface; a bearing (18a, 18b, 18c) externally fitted to a tip part of the worm; and an inner diameter side holder (25, 25a, 25b, 25c) including a bearing holding part in which the bearing (18a, 18b, 18c) is internally fitted and held; characterized in that, the worm reduction gear further comprises: an outer diameter side holder (26, 26a, 26b, 26c, 26d, 26e) internally fitted and held in the holding recessed part, including a holder holding part (38a, 38b) in which the inner diameter side holder (26, 26a, 26b, 26c, 26d, 26e) is internally fitted and held so as to be able to be relatively rotated and moved and to be displaced in a direction orthogonal to a center axis of the worm wheel and a center axis of the worm; and an elastic urging member (28, 28a, 28b, 28c) in a circumferential direction elastically urging the inner diameter side holder (25, 25a, 25b, 25c) against the outer diameter side holder (26, 26a, 26b, 26c, 26d, 26e) in a direction of rotating in the circumferential direction, wherein when the inner diameter side holder (25, 25a, 25b, 25c) rotates in the circumferential direction with respect to the outer diameter side holder (26, 26a, 26b, 26c, 26d, 26e), an outer circumferential surface of the inner diameter side holder (25, 25a, 25b, 25c) and an inner circumferential surface of the outer diameter side holder (26, 26a, 26b, 26c, 26d, 26e) are formed so that the bearing (18a, 18b, 18c) is displaced in the direction orthogonal to the center axis of the worm wheel and the center axis of the worm. an outer diameter side holder (26, 26a, 26b, 26c, 26d, 26e) internally fitted and held in the holding recessed part, including a holder holding part (38a, 38b) in which the inner diameter side holder (26, 26a, 26b, 26c, 26d, 26e) is internally fitted and held so as to be able to be relatively rotated and moved and to be displaced in a direction orthogonal to a center axis of the worm wheel and a center axis of the worm; and an elastic urging member (28, 28a, 28b, 28c) in a circumferential direction elastically urging the inner diameter side holder (25, 25a, 25b, 25c) against the outer diameter side holder (26, 26a, 26b, 26c, 26d, 26e) in a direction of rotating in the circumferential direction, wherein when the inner diameter side holder (25, 25a, 25b, 25c) rotates in the circumferential direction with respect to the outer diameter side holder (26, 26a, 26b, 26c, 26d, 26e), an outer circumferential surface of the inner diameter side holder (25, 25a, 25b, 25c) and an inner circumferential surface of the outer diameter side holder (26, 26a, 26b, 26c, 26d, 26e) are formed so that the bearing (18a, 18b, 18c) is displaced in the direction orthogonal to the center axis of the worm wheel and the center axis of the worm.