Indicatrices of the light scattering on homogeneous nanoparticles with radii of r (0) = 50, 75, and 100 nm and on double-layer nanoparticles with core radii of r (0) = 40, 65, and 90 nm and a shell thickness of Delta (r) = 10 nm are calculated numerically for light wavelengths of lambda = 300, 560, and 1000 nm. Metals Ti, Ni, and Zn and their oxides, TiO2, NiO, and ZnO, were used as materials for homogeneous nanoparticles. The same metals and their oxides were used, respectively, as materials for the core and the shell of the double-layer nanoparticles. It is shown that, in comparison with the pure metal or pure oxide dielectric nanoparticles, the presence of the oxide shell on the titanium and nickel cores leads to a significant decrease in the backscattering for lambda = 300 nm.