Abstract: A clutch assembly is preferably designed as a multiple-disc clutch. Rotating with one clutch half (22) is a clutch-engaging piston (26) and a pressure chamber (25) into which fluid may be admitted. Against the force of a spring (29), the piston may be subjected to the fluid pressure which is generated in the pressure chamber (25) and which is dependent upon the rotational speed. Arranged beside the pressure chamber is a fluid reservoir chamber (37), communicating with the pressure chamber (25) via connecting conduits (44, 45). With the aid of a control element (48) the filling of the pressure chamber (25) with fluid from the reservoir chamber (37) is controlled during a start-up process. In this manner, the engagement of the clutch assembly is controlled. Thereby delivery of fluid from outside of the clutch assembly is unnecessary.