The frequencies of the vibrational modes of CdTe and CdSe quantum dots and CdTe/CdSe core/shell nanoparticles prepared by the colloidal chemistry method are determined using IR transmission and IR reflection spectroscopy. The experimental IR transmission spectrum of CdTe and CdSe nanocrystals exhibits a broad minimum located between the frequencies of the transverse (TO) and longitudinal (LO) optical phonons of bulk CdTe and CdSe crystals. The frequencies of the modes for ensembles of CdTe and CdSe quantum dots are considerably shifted toward lower frequencies as compared to those calculated for single quantum dots. This is explained by the dipole-dipole interaction between quantum dots. The frequencies of modes for the structures with core/shell nanoparticles differ little from the calculated frequencies. This suggests a weakening of the interaction in these structures due to the enhancement of dielectric screening.