The invention relates to a clutch assembly of a motor vehicle, in particular to a clutch-controlled differential unit, having a switchable clutch device which can transmit the drive power from a drive element which is at the drive input side in relation to the clutch device to a drive element which is at the drive output side in relation to the clutch device, wherein an oil delivery device is provided for the oil lubrication of the clutch, which oil delivery device, in an operating-state-dependent manner, delivers oil of an oil circuit which serves the clutch device. The clutch assembly is mounted in a housing which forms a clutch chamber for the clutch device. In order to permit rapid deoiling of the clutch chamber in situations in which the clutch device is opened, a deoiling device is provided which actively deoils the clutch chamber when the deoiling unit is not imparting a delivery action.