The crystallization kinetics and morphology of biodegradable and double crystalline poly(L-lactide)-b-poly(epsilon-caprolactone) diblock copolymers (PLLA-b-PCL) was studied in a wide composition range by differential scanning calorimetry (DSC) and polarized light optical microscopy (PLOM). The two blocks were found to be partially miscible according to the variations of their thermal transitions with composition. PLOM results showed that PLLA crystallizes in a wide composition range with a spherulitic superstructural morphology. Only when the PLLA content is as low as 10 wt % are axialites formed. These results were in good agreement with the overall crystallization kinetics obtained by DSC isothermal experiments and analyzed by the Avrami equation. Both overall crystallization rates and spherulitic growth rates of the PLLA block decrease with PCL content because PCL acts as a diluent for the PLLA block in view of their miscibility. Reorganization processes revealed as double melting peaks for the PLLA block (not observed for the PLLA homopolymer) were observed during heating scans performed after isothermal crystallization. The reorganization ability of the PLLA block was found to increase with PCL content, a fact that quantified the perturbation caused by molten PCL, block chains during the isothermal crystallization of the PLLA block. The PCL block crystallizes within previously formed PLLA spherulites or axialites. Despite the partial miscibility, unexpected and novel fractionated crystallization of the PCL occurs at contents of PCL, between 40 and 19 wt %. For the lowest PCL content (i.e., 19%), a homogeneous nucleation process was detected, as indicated by the large supercooling needed for crystallization and by the first-order crystallization kinetics obtained (i.e., Avrami index close to 1). Because of the partial miscibility, the glass-transition temperature of the PLLA block (T-g,T-PLLA) decreases with PCL addition, so at PCL contents lower than 40 wt %, the T-g,T-PLLA values are close to or higher than the crystallization temperature of the PCL block. Therefore, PCL fractionated crystallization is induced by hard confinement of the PLLA amorphous and crystalline regions. This is the first time that a homogeneous nucleation process has been documented for a crystallizable component in a miscible or weakly segregated diblock copolymer. The PCL block can also be nucleated by previously formed PLLA crystals depending on the crystallization degree of the PLLA, which was varied by self-nucleation experiments. The crystallization rate of PCL strongly decreased with increasing PLLA content.