To provide a clutch device for a car air-conditioner which is simple, compact, lightweight and unnecessary for any auxiliary power such as the electromagnetic force of an electromagnetic clutch.

When an input pulley 8 is turned, an outer ring 2 of a clutch is rotated by a plate 5 connected thereto, and a screw plate 18 is driven in the axial direction in an interlocking manner via a connection rod 6 of the outer ring 2. When a feed screw plate 18 is rotated, the outer ring 2 is displaced in the axial direction by an axial displacement generating screw 14 via a rod 6, the outer ring 2 is attached/detached to/from a roller 3 to turn ON/OFF the drive of a compressor input shaft 4.