It was generally accepted that metal covered inclusions in a dielectric host matrix havernone maxima of the enhancment factor at one resonant frequency close to the frequency ofrnthe surface plasmon. Recently,Sisay shewamare, V.N.Mal'nev with coauthors have shownrnthat the local eld in the metal covered nanoinclusion with small dielectric core has twornmaxima at two di erent resonant frequencies. The second maxima is not important inrnmetal covered inclusions with small dielectric cores. But for large metal fractions, thernmaxima of the enhancment factor become the same order of magnitude and must berntheken into account.rnThe aim of this thesis is to check the dependence of the resonant frequencies and thernenhancment factor of the local eld on the parameters of the composite(metal frac-rntion,dielectric function of the core, metal shell, and host matrix) in the spherical in-rnclusions. And the second objective of the thesis is to calculate the above mention physicalrnquantites in the composites with cylinderical inclusions. The account of two maxima ofrnthe enhancment factor of the local eld a ects the linear and non linear optical propertiesrnof the composites metal inclusions having small dielectric cores