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n this work, within the framework of the effective medium method, we study the influence of various microscopic parameters, semi-classical and quantum size effects on the magneto-optical spectra of the equatorial Kerr effect of magnetic nanocomposites (CoFeZr)x ( Al2 O3 )1− х, (Co)x ( Al2 O3 )1−х , (Co)x (SiO¿ ¿ 2)1− x , ¿ (CoFeB)х(LiNbO3)1-х and two-layer NiFe/Ta structures. The calculations took into account the possibility of spin-orbit interaction enhancement in a thin near-surface layer, which affects both interband and intraband optical transitions.