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Resonance Raman spectra and excitation profiles have been measured and semiquantitatively modeled for core/shell quantum dots consisting of 2.7 nm diameter zincblende CdSe cores and thin (0.5 nm) or thick (1.6 nm) CdS shells. The Raman spectra show previously reported trends of increased peak frequency for both the CdSe and the CdS longitudinal optical (LO) phonons with increasing shell thickness. We also find a strong dependence of the peak CdS frequency on excitation energy and a large discrepancy between the experimental frequency of the CdSe + CdS combination band and the sum of the corresponding fundamental frequencies. This suggests that the dominant transitions at high excitation energies are localized on either the CdSe core or the CdS shell and thereby cannot enhance combination band transitions between core and shell. The CdS to CdSe Raman intensity ratios at high excitation energies further support this picture. The electron-phonon coupling for the CdSe LO phonon in the lowest excitonic transition is slightly weaker in the core/shell structures than in pure CdSe quantum dots, contrary to expectations for the Fröhlich coupling mechanism. Possible explanations for this discrepancy are discussed.