The electronic states of “wurtzite” CdS nanoparticles and CdSe/CdS nanosystems with up to 80 pairs of Cd-Se or CdS atoms were calculated.The results for CdS particles were compared with the results obtained earlier for CdSe particles of the same size and with published calculations of other authors. The calculated gap values in the range of 2.84 eV ~ 3.78 eV are typical for CdS particles of studied sizes in accordance with results of published data. The CdSe/CdS nanosystems were considered as layered ones and as quantum dots. The layered CdSe/CdS systems with twolayer CdS coverings can be interpreted in terms of combinations of two semiconductors with different energy band gaps (2.6 eV and 3.3 eV), while analogous systems with single-layer CdS coverings do not demonstrate a two-gap electron structure. Simulation of a CdSe/CdS quantum dot shows that the single-layer CdS shell demonstrates a tendency for the formation of the electronic structure with two energy gaps: approximately of 2.5 eV and 3.0 eV.