The physical ageing of poly(L-lactic acid) (PLLA) samples crystallized in a wide temperature range, is compared, through the analysis of the enthalpy relaxation, with the behavior of a completely amorphous sample, in the same undercooling conditions. A preliminary determination of the percentage of the different phases in the semi-crystalline samples (crystalline, mobile amorphous and rigid amorphous fractions) has been performed. The enthalpy loss (Delta h(a)), normalized to the mobile amorphous content, has allowed to differentiate PLLA samples crystallized at different temperatures, because the samples crystallized at lower temperatures, characterized by a slightly constrained mobile amorphous fraction, exhibit a smaller enthalpy loss. In addition, the normalized Delta h(a) data relative to the semi-crystalline PLLA samples have been found to deviate from the Delta h(a) values of the amorphous sample at high undercooling. This trend has been ascribed to the contribution of the rigid amorphous fraction to the structural relaxation process. The experimental data have been explained by supposing that structural relaxation in amorphous and semi-crystalline PLLA occurs at low undercooling via cooperative segmental motions, whereas, at high undercooling, through small-scale local motions, which take place also in the rigid amorphous fraction. (C) 2017 Elsevier Ltd. All rights reserved.