In a mechanism for driving motor vehicles having a synchromesh gearbox with a friction clutch for each of two power branches with at least four power shiftable speeds and consecutive speeds are alternatively present on each one of the two power branches. Each friction clutch is a wet disc clutch with its inner discs having continuous radial grooves for a cooling oil flow supplied from a bore in a shaft. A switch piston shuts off the flow of cooling oil when the friction clutch is disengaged or almost completely disengaged. A prestressed cup spring in a compensating cylinder serves as a strong return spring thereby accelerating disengagement or delaying engagement of the friction clutch. Corrugated spring rings, axially situated between the inner discs and radially within the outer discs, serve as additional return springs. The wet clutch operates as a dry clutch and only has a low torque when it is disengaged. A large flow of cooling oil flows to the friction clutch and cools it as it engages and when it is engaged. The wet friction clutch replaces a conventional dry friction clutch, especially when starting up the motor vehicle.
