Enthalpy relaxations during physical ageing have been examined for two amorphous poly(ethylene terephthalate) (PET) samples with different thermo-mechanical glass-forming histories by differential scanning calorimetry. The relaxation behaviour of the PET glass formed by casting the drawn melts on a metal roller at 10-degrees-C can be explained from a molecular viewpoint, assuming that the glass consists of a network structure with strand chains and crosslinks. It is shown that the physical ageing of the glass gives rise to three different modes of structural rearrangement : (i) strand chain relaxation with relatively short relaxation times, associated with local segmental rearrangements within the strand chains; (ii) enthalpy redistribution, which forms the non-homogeneous dissipative structures of lower- and higher-enthalpy regions; and (iii) network rearrangements taking place slowly with long-distance, diffusive motions of the crosslinks. On the other hand, it is also shown that a single mode of structural rearrangement occurs for the ultraquenched PET glass formed by quenching directly into liquid nitrogen.