A drive train, which has an internal combustion engine with a crankshaft and a parallel shift transmission with two part drive trains, which each have one transmission input shaft. One shaft is formed as a hollow shaft around the other shaft, and a dual clutch, which is received rotatably on the hollow shaft, is connected to the crankshaft and has two friction clutches and two clutch plates each assigned to one clutch and are each connected to one transmission input shaft. Each clutch plate has a torsional vibration damper with a working range which is smaller than a maximum torque of the engine. A build-up of a combined vibration which has an axial vibration of the dual clutch and a rotational vibration of the drive train during an overlap shift operation is prevented by the design of the torsional vibration dampers for a smaller torque.