To exhibit a constant damping function stably just after assembling insert bearings in an auto-tensioner which is constituted so that rotation in the opposite direction to the rotation energizing direction of a rotating member may be damped by pressing the boss part of the rotating member against the insert bearing externally fitted so as not to rotate on the shaft part of a stationary member by means of the reaction force of a torsion coil spring and using sliding friction force generated between both of them.

When both the inner periphery surface of a boss part and the outer periphery surface of an insert bearing 11 are of tapered shape in cross section with the front end side of its shaft part set at a small diameter, a clearance on the base end side of the shaft part between the boss part and the insert bearing 11 is set smaller than that on the front end side of the shaft part by setting a taper angle of the base end side of the shaft part of the outer periphery surface of the insert bearing 11 larger than the taper angle of the front end side of the shaft part.