The remarkable energy absorption capacity of nonwovens has been used for years in a variety of applications where acoustic or impact damping is required. Although it seems likely that the superior energy absorption capacity could also be used for structural dynamic damping, there are only a few publications on the use of nonwovens or dry fibre assemblies for vibration damping. Our experimental investigations show that nonwovens exhibit excellent damping properties under shear deformation due to numerous frictional contacts of their fibrous constituents. The investigations also reveal a strong dependence of the damping behaviour on material compression, which can enable a new class of adjustable dampers based on the constrained layer damping principle. The dynamic behaviour of a structure could be semi-actively tuned by in operando compression of the damping material. The damping properties of four exemplary nonwoven materials were assessed using oscillatory rheology experiments, which allow a direct measurement of the phase shift between the applied sinusoidal strain and the stress response. From this data, storage and loss modulus as well as the dissipated energy per cycle were calculated. The samples were compressed to a range of compression levels and tested at four different strain amplitudes. It has been observed that the damping capacity of the nonwovens tested differs considerably and depends on the compression level. Compared to a widely used CLD foil, nonwovens can dissipate up to seven times more energy per cycle. As expected, the coating of the fibres has a major influence on the dissipated energy. Therefore, it is even possible to further increase the damping performance by a special fibre surface treatment.