The present invention relates to a multiple clutch device having a first clutch which is assigned a first actuating piston with a first pressure chamber and a first pressure equalization chamber, and having a second clutch which is assigned a second actuating piston with a second pressure chamber and a second pressure equalization chamber, a first crossflow channel WO being provided for setting the hydraulic fluid column in the first pressure equalization chamber and a second crossflow channel being provided for setting the hydraulic fluid column in the second pressure equalization chamber. According to the invention, the first and second crossflow channels are arranged in such a way that both the oil which is discharged via the first crossflow channel and the oil which is discharged via the second crossflow channel can be fed to the first and second clutches.