Dielectric and mechanical relaxation spectroscopy of thermoplastics and thermosets show that, in the former, ageing is related only to the spontaneous structural relaxation towards a lower energy, but still disordered, structure and decreases the strength of the β- relaxation process. Ageing of a thermoset initially increases the strength of its (dielectric) β-relaxation as a result of diffusionallowed chemical reactions, which increase the number of dipolar groups, and later decreases it towards a limiting value. The decrease in the strength of β-relaxation on ageing of polymers and other amorphous solids suggests that structural relaxation causes a collapse of low-density, high-entropy, regions or “soft-sites” randomly distributed in the structure of a glassy material. The increase in the strength of β-relaxation observed in thermosets is higher than calculated from the extent of chemical reactions that occur during their structural relaxation at T<Tg. It is suggested that these effects should be included in the phenomenological theories for both the physical ageing and “memory behaviour” - the latter can be conveniently studied by both dielectric and mechanical spectroscopy and by differential scanning calorimetry. Structural relaxation also decreases the magnitude of the specific heat anomaly in amorphous solids and can be used to experimentally test the postulate that tunneling centres involved in the low-temperature phonon properties are related to the presence of “islands of mobility” or “soft-sites” in an otherwise rigid glassy matrix.