The invention is directed to a multiple-clutch device, such as a double-clutch device, for arranging in a drivetrain of a motor vehicle between a drive unit and a transmission, wherein the clutch device has a first clutch arrangement associated with a first transmission input shaft of the transmission and a second clutch arrangement associated with a second transmission input shaft of the transmission for transmitting torque between the drive unit and the transmission. According to one aspect of the invention, it is suggested that at least one of the clutch arrangements is constructed as a plate clutch arrangement and has an actuating piston defining a pressure chamber for actuation, preferably for engagement, of the plate clutch arrangement by means of a pressure medium, preferably hydraulic medium, wherein cooling fluid, possibly cooling oil, can be supplied to the plate clutch arrangement from a cooling fluid supply, possibly a cooling oil supply, wherein the actuating piston, and also, if desired, a plate carrier, possibly an outer plate carrier, has at least one pressure compensation opening and/or cooling fluid outlet opening in a radial outer and/or central area.