The study of the electrodynamics properties of small spherical particles with a nonlinear dielectric and covered by the metal shell shows that the IOB (induced optical bistability) in this type of inclusion may emerge in two-frequency bands. This methods of study will help in the experimental research to determine the range of applied frequency and to get the optimum output frequency. It help us to calculate the real and imaginary parts of the refractive index of the composites of spherical metal inclusions with small dielectric cores and for a pure metal embedded in equilibrium host matrix and active host matrix.