Abstract Healing of interfaces of amorphous and semi-crystalline poly(ethylene terephthalate) (PET) was carried out above and below the (bulk) glass transition temperature (Tg) of the samples (two amorphous and two semi-crystalline polymers of different molecular weights). The lap-shear strength of the amorphous/amorphous interface was found to develop without discontinuity in the vicinity of the Tg and, in addition, it develops at amorphous/amorphous and amorphous/crystalline interfaces to the one-fourth power of healing time indicating that it is, in both cases, a diffusion controlled process. Similar values of strength were found with these two interfaces whereas the strength at the crystalline/crystalline interface of PET was at least one order of magnitude lower after healing under the same conditions. However, the largest values of strength were obtained by a procedure where diffusion is followed by crystallisation. These results were compared with those measured for an amorphous and incompatible PS/PET interface, below and above the Tgs of PS and PET, and it was found that the strength of the incompatible PS/PET interface is close to the strength of the compatible PET/PET interface. A comparison of the strength developed at symmetric amorphous interfaces of crystallisable PET and non-crystallisable atactic PS showed a more rapid growth in strength in the second case, even at temperatures below Tg.