To provide a rotation control damper that can prevent a rotor from slipping out of a stator and make the rotation of the rotor always smooth so as to prevent lowering of rotational torque by making both axes of the stator and rotor automatically coincide with each other.

A rotation control damper is composed of a rotor 19 formed of a spur gear 15 and a plurality of concentric rotating cylinder parts 16 provided on the back face of the spur gear 15, and a stator 20 formed of a plurality of concentric fixed cylinder parts 19 rotatably fitted to the rotating cylinder parts 16. An annular protruding part 24 is formed at the outer peripheral surface of an outer ring cylinder part 21C positioned on the outermost side of the rotating cylinder parts 16 of the rotor 17, and an engaging protruding part 26 fittable to the annular protruding part 24 and slidable in a rotating direction is formed at a base on the outside of an inner ring cylinder part 22C positioned on the outermost side of the stator 20. A down inclined face descending obliquely downward is formed at least at either one of the contact parts of the annular protruding part 24 and engaging protruding part 26, and oil 28 is interposed in a clearance between the rotating cylinder parts 16 and fixed cylinder parts 19.