Polystyrene-block-poly(ethylene-co-butylene)-block-poly(epsilon-caprolactone) triblock copolymers (SEC) mere prepared by hydrogenating polystyrene-block-polybutadiene-block-poly(epsilon-caprolactone) triblock copolymers (SBC) previously prepared by sequential anionic polymerization. The effect of the crystallization of the polyethylene block (PE) upon cooling from a phase-segregated melt on the crystallization process of the adjacent polycaprolactone block (PCL) was investigated by means of differential scanning calorimetry and polarized optical microscopy. It was found that there was no nucleation effect of the PE block on the PCL block under controlled cooling conditions in the DSC. On the contrary, an antinucleation effect was detected when nucleation of the PCL block crystals within the SEC triblock copolymers was attempted. It was demonstrated that such an antinucleation effect was induced by the annealing of the polyethylene block crystals of the SEC copolymers. By the application of the successive self-nucleation and annealing technique (SSA) the possibility of producing a distribution of lamellar thickness within the PCL and the PE blocks of the SEG triblock copolymers was shown. These results, together with the spherulitic morphology displayed by the SEC copolymers with more than 50 wt.-% PCL, are consistent with previous morphological observations in SEC triblock copolymers. Those observations indicate that the chain stems within the lamellar crystals in the PCL blocks could be perpendicular to the interphase of the block copolymer domains, even though the crystallization occurred from a heterogeneous melt.