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We have investigated the phonons contribution in the infrared and visible optical properties in II-VI semiconductor nanoshells of type I. For this, we use Mie scattering theory by defining appropriate dielectric functions for the constitutive materials of the nanoshells. Indeed, for the core we have considered dielectric function taking into account the spatial confinement of the charge carriers along with the phonons contribution. For the shell, we have considered dielectric function similar to that used in bulk semiconductor. Independently of the core and shell sizes and the embedding medium, we obtain in the infrared (IR) spectra, three resonant peaks ascribed to the CdS stretching vibration, the longitudinal optical (LO)-CdS and surface optical (SO)-ZnS phonon modes, respectively. The increase of core and shell sizes induces a red shift of the Cd-S stretching vibration and the SO ZnS branches, while a blue-shift is obtained for the LO CdS branch. If the phonons contribution is not considered in the IR spectrum, the CdS stretching vibration is disappeared. On the other hand, in the visible (VIS) spectra, we obtain one sharp resonant peak related to the 1s(e)-1s(h) optical transition, whose localization is characterized by the core size, essential parameter to evaluate the exciton energy. Phonons contribution in the VIS range yields information about the exciton-phonon coupling in II-VI semiconductor nanoshells. When the embedding medium is glass, where the dielectric constants at high frequency of core, shell and islanding materials are similar, we obtain two effects on the IR as well as the VIS optical properties: (i) the phonon peaks (IR range) or the exciton peak (VIS range) are red-shifted, and (ii) the peaks intensities are greater. Therefore, in the light of these results, it can be concluded that the phonons contribution is primordial if the optical properties are investigated in the low-dimensional systems.