An angular position holding apparatus for applying a braking torque to hold a position of an output-side device when no rotation torque is input from an input-side device, the angular position holding apparatus comprises an outer race member and an inner race member each rotatable about a common central axis and each having an outer peripheral surface with circular cross section, either the outer race member or the inner race member is connected to the input-side device while the other is connected to the output-side device, a coil spring is mounted on the outer peripheral surface of the outer race member, the coil member in a free state has an inner diameter smaller than the outer diameter of the outer race member, the coil spring has hooks (68a, 68b) at the both ends that are locked to a fixed member, a predetermined braking torque is applied to the outer race member by a tightening force of the coil spring, an internal space having a circular cross section to accommodate the inner race member is formed in the outer race member, and a cylindrically-rolled thin-plate elastic piece is installed between the inner peripheral surface of the outer race member and the outer peripheral surface of the inner race member so that the thin-plate elastic piece is brought into contact with the inner peripheral surface and the outer peripheral surface, the thin-plate elastic piece and the coil spring are installed collectively at the same position in the axial direction of the outer race member, the outer race member and the inner race member rotate integrally against the braking torque when a rotation torque input from the input-side device is larger than the braking torque, and the connection by the thin-plate elastic piece between the outer race member and the inner race member is cut off to make the outer race member and the inner race member rotate relatively when a rotation torque larger than the braking torque by at least a predetermined value is generated between the outer race member and the inner race member. the angular position holding apparatus comprises an outer race member and an inner race member each rotatable about a common central axis and each having an outer peripheral surface with circular cross section, either the outer race member or the inner race member is connected to the input-side device while the other is connected to the output-side device, a coil spring is mounted on the outer peripheral surface of the outer race member, the coil member in a free state has an inner diameter smaller than the outer diameter of the outer race member, the coil spring has hooks (68a, 68b) at the both ends that are locked to a fixed member, a predetermined braking torque is applied to the outer race member by a tightening force of the coil spring, an internal space having a circular cross section to accommodate the inner race member is formed in the outer race member, and a cylindrically-rolled thin-plate elastic piece is installed between the inner peripheral surface of the outer race member and the outer peripheral surface of the inner race member so that the thin-plate elastic piece is brought into contact with the inner peripheral surface and the outer peripheral surface, the thin-plate elastic piece and the coil spring are installed collectively at the same position in the axial direction of the outer race member, the outer race member and the inner race member rotate integrally against the braking torque when a rotation torque input from the input-side device is larger than the braking torque, and the connection by the thin-plate elastic piece between the outer race member and the inner race member is cut off to make the outer race member and the inner race member rotate relatively when a rotation torque larger than the braking torque by at least a predetermined value is generated between the outer race member and the inner race member.