A hydrostatic continuously variable transmission includes a hydraulic pump and a hydraulic motor, supported by a common support shaft, and hydraulically connectable to each other through a hydraulic circuit including an inside passage and an outside passage. A clutch device includes a valve spool, which is slidably disposed in a hollow internal bore formed in the transmission support shaft. The valve spool is operable to make or interrupt fluid communication between the inside passage and the outside passage, according to the movement thereof. A governor mechanism is mounted to a pump casing of the hydraulic pump, and the governor mechanism generates a governor force corresponding to the rotating speed of a clutch cap, by use of centrifugal force generated by the rotation thereof. The valve spool is effectively moved in the hollow internal bore, using the governor force generated from the governor mechanism, to engage or disengage the clutch.