Apparatus for damping torsional vibrations in the power train of a motor vehicle has a first flywheel which defines an annular chamber for a supply of viscous fluid medium and carries one sealing device of a composite seal for separation of the chamber from the atmosphere. A second flywheel carries an antifriction bearing and the second sealing device of the composite seal. The first flywheel and the first sealing device form component parts of a first subassembly. The second flywheel, the second sealing device and the bearing form parts of a second subassembly. The two subassemblies are connected to each other in that the inner race of the bearing is slipped onto a cylindrical seat on an axial protuberance of the first flywheel and is retained on the protuberance of a ring which is affixed to the protuberance and overlies the inner race of the bearing. A torque-transmitting coupling between the second flywheel and the flange-like output member of a single damper or of two parallel-connected dampers in the chamber becomes operative in automatic response to attachment of the two subassemblies to each other.