Formulas are obtained for the effective relaxation time when the electron mean free path is less or comparable with the characteristic dimensions of the metallic regions. The frequency dispersion of the optical characteristics of spherical bimetallic particles near plasma resonances is calculated in the absence of quantum-size effects. Maintaining the style of the generally accepted description of monometallic particles based on the theories of Drude and Mie, the frequency dependence of the electric dipole polarizability of a two-layer metal nanosphere is analyzed. The appearance of two maxima of polarizability is a consequence of the difference between the metals of the core and the shell. The calculations were performed for Au @ Ag, Ag @ Au, Au @ Pt, Pt @ Au, and Pt @ Pd particles immersed in Teflon. The possibility of controlling the optical characteristics of bimetallic particles by changing their composition and volumetric content of metals has been demonstrated. The calculations of the absorption and scattering cross sections, as well as the optical radiation efficiency of particles in a wide spectral range, have been performed. The possible temperature of bimetallic particles upon absorption of an electromagnetic wave (for the purposes of photothermal therapy of malignant tumors) has been estimated. Key words: bimetallic nanoparticle, surface plasmon, polarizability, absorption cross section, scattering cross section, relaxation time.