Abstract
The ways and peculiarities of the application of the hierarchic theory of nonlinear oscillations and methods of averaging in problems of relativistic electrodynamics are given. By using the motion of charged particles and beams in periodic electromagnetic fields as an basis example the theory of the nonlinear hierarchic oscillations are formulated. Effectivity and possibilities of the described approaches are illuatrated by the examples of single particle and selfconsistance theories of the parametrical and superheterodyne free-electron laser, the theory of the EH-accelerators. The material of the article is presented in a form of general theory of relativistic electronic devices with protracted interaction, which some methodical peculiarities are illustrated by concrete partial examples.
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