A hydraulically operated continuously variable transmission for an automobile includes a hydraulic pump coupled to an input shaft and having an outlet port, a hydraulic motor coupled to an output shaft, at least one of the hydraulic pump and the hydraulic motor being of the variable-displacement type, a closed hydraulic circuit interconnecting the hydraulic pump and the hydraulic motor, and a device for selectively making and breaking the hydraulic circuit respectively by opening and closing the outlet port. The device comprises a valve body for closing the outlet port, a valve holder for driving the valve body to selectively open and close the outlet port, and a spring for normally urging the valve body in a direction to close the outlet port, the valve body and the valve holder being held in engagement with each other for relative displacement in directions to open and close the outlet port.