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 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 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 . <EOS>