The magnitude of torque which can be transmitted by a bypass clutch between the housing and the turbine of a torque converter between a prime mover, such as an engine, and an automatic transmission in the power train of a motor vehicle is selectively regulatable by a computerized regulating unit. The regulation involves the transmission of torque by the clutch in dependency upon the magnitude of the torque being transmitted by the output element of the engine and ascertaining as well as adaptively applying to the clutch a variable force so that the clutch can transmit a predetermined torque. This entails automatic selection of a minimum slip between a torque receiving and a torque transmitting part of the power train. Compensation, particularly long-range compensation, is carried out for the existence of possible differences between the predetermined and actual torques being transmitted by the clutch.