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The open problem of derivation of the relativistic Vlasov equation for thesystems of charged particles moving with the velocities up to the speed oflight and creating the electromagnetic field in accordance with the full set ofthe Maxwell equations is considered. Moreover, the method of derivation isfirstly illustrated on the nonrelativistic kinetic model. Independentderivation of the relativistic hydrodynamics is also demonstrated. Key role ofthese derivations of the hydrodynamic and kinetic equations includes theexplicit operator of averaging on the physically infinitesimal volume suggestedby L.S. Kuzmenkov.

Hydrodynamic and kinetic representation of the microscopic dynamics as  the transitions on the macroscopic scale of description and meaning of the  self-consistent field approximation in these models