To provide a damping device easily applicable to, for example, a steering damper of a motorcycle, not requiring any special installation space, not causing an interference with the other on-vehicle part, and not damaged by external force.

This damping device is so formed that an outer member 6 and inner members 1 and 2 are disposed rotatably relative to each other around a rotating axis to generate a damping force corresponding to the relative rotation of these both members. The inner members 1 and 2 are co-axially disposed in the outer member 6, and operating chambers 12 and 13 having volumes varying according to a change in the relative rotating angles thereof are formed of the outer member 6 and the inner members 1 and 2. A working medium 14 is filled in the operating chambers 12 and 13 so that damping force can be generated by the movement of the working medium 14 according to the volumetric change of the operating chambers 12 and 13.