A torsional vibration damper, particularly for use between the engine and the transmission of the power train in a motor vehicle, including two flywheels rotatable relative to each other against the opposition of a first energy storing device employing, for example, one or more coil springs and a second energy storing device, which is carried by one of the flywheels, which operates in parallel with the first energy storing device and which opposes rotation of the two flywheels relative to each other. In order to isolate the irregularities of movement of the first flywheel (such as vibrations which develop while the engine is in operation) from the second flywheel, the second energy storing device (such as a snap spring or a set of diaphragm springs) is coupled to the flywheels in such a way that the second flywheel develops a degressive action only when the first flywheel is caused to move through relatively small angles (especially between 1.degree. and 10.degree.) but not when the angles are larger (especially larger than 10.degree.).