A parallel double-clutch device is arranged in a drivetrain of a motor vehicle between a drive unit and transmission of the drivetrain. The device comprises a first clutch arrangement assigned to a first transmission-input shaft for selectively transmitting torque between the drive unit and first transmission-input shaft. A second clutch arrangement is assigned to a second transmission-input shaft for selectively transmitting torque between the drive unit and second transmission-input shaft. The first clutch arrangement can be actuated by at least one hydraulically drivable first actuating piston assigned a first pressure chamber delimited by a first pressure-chamber housing and the first actuating piston. The second clutch arrangement can be actuated by at least one hydraulically drivable second actuating piston assigned a second pressure chamber delimited by a second pressure-chamber housing and the second actuating piston. The pressure-chamber housing is at least partially substantially stationary and/or rotationally fixed.