An alternating multiblock copolymer of poly(epsilon -caprolactone) (PCL) and poly(hexamethylene terephthalate) (PHT) with a 48/52 PCL/PHT composition weight ratio has been synthesized. Its structural and morphological parameters were measured using H-1 NMR, density measurements, differential scanning calorimetry and its crystallization and melting were studied by real time simultaneous WAXS and SAXS using synchrotron radiation. These results are compared with those for the pure PCL and PHT used as building blocks. In the crystallization conditions used here, the copolymer crystallizes as alternate lamellae of PHT and PCL. The crystallinity of the PCL blocks is much lower than that of pure PCL because they crystallize under stress in the semi-crystalline PHT network.