PET and PLLA were cold crystallised at various times and the two polymers were studied by differential scanning calorimetry (DSC), dielectric spectroscopy (DS) and thermally stimulated depolarisation currents (TSDC). The crystalline, the amorphous and the rigid amorphous fraction were quantified. The percentage of rigid amorphous fraction is very large in semi-crystalline PET and very low in semi-crystalline PLLA. From DSC, DS and TSDC data, the values of the relaxation times of four samples were obtained above and below the glass transition. The "strong-fragile" glass former liquid concept was used and the fragility of polymers was obtained. The presence of the crystalline phase and of a rigid amorphous fraction does not significantly modify PLLA fragility parameters and the polymer remains "fragile", while for PET the semi-crystalline material goes towards a "strong character". The coupling between phases is much weaker in PLLA than in PET. (c) 2007 Elsevier Ltd. All rights reserved.