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We report on the band edge alignment in zinc-blended-type CdTe/CdS core-shell quantum dots, using femtosecond spectroscopy. Time-resolved transient absorption spectroscopy directly shows that the system gradually developed from quasi-type-I to type-II as the shell thickness increased. Following photoexcitation of CdS, the injection of a hole from CdS valence band into CdTe valence band is observed. The hole transfer occurs on the 1000 fs time scale in these heteromaterials. Furthermore, a strain ca. 150 meV is obtained by comparing the transient with steady-state spectra.