The morphology, crystallization and self nucleation behavior of double crystalline diblock copolymers of poly(p-dioxanone) (PPDX) and poly(ε-caprolactone) (PCL) with different compositions have been studied by different techniques, including optical microscopy (OM), atomic force microscopy (AFM) and differential scanning calorimetry (DSC). The two blocks crystallize in a single coincident exotherm when cooled from the melt. The self-nucleation technique is able to separate into two exotherms the crystallization of each block. We have gathered evidences indicating that the PPDX block can nucleate the PCL block within the copolymers regardless of the composition. This effect is responsible for the lack of homogeneous nucleation or fractionated crystallization of the PCL block even when it constitutes a minor phase within the copolymer (25% or less). Nevertheless, we were able to show that decreasing amounts of PCL within the diblock copolymer still produces confinement effects that retard the crystallization kinetics of the PCL component and decrease the Avrami index. On the other hand evidence for confinement was also obtained for the PPDX block, since as its content is reduced within the copolymer, a depression in its self-nucleation and annealing temperatures were observed.