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In the framework of the many-electron s-d exchange model and Hubbard model,self-consistent equations are derived for the one-particle retarded Green'sfunction in the many-electron Hubbard X-operator representation. We analyze thegeneral structure of the single-site approximations and their connection withthe coherent potential approximation (CPA) and dynamic effective field theory(DMFT). Using the self-consistent approximation, we examine in detail thepicture of the evolution of the electron spectrum with the model parameters(coupling constants, the concentration of charge carriers). The influence ofvarious factors (Kondo many-electron scattering, smearing due to damping,dynamics of localized moment subsystem) on the shape of the density of statesN(E) in the interacting system is investigated. It is shown that the use of thelocator representation allows to avoid in some cases the non-analyticity inapproximate expressions for the Green's functions. Our approach enables one toreproduce, at certain values of the parameters, three-peak structure of N(E)near the metal-insulator transition.

Evolution of the spectrum and the metal-insulator transition in local approximations for many-electron models