In the paper a method of solution of the problem of non-stationary motions of a plasma in the external electromagnetic field has been given. As starting equations the transport equations for ions and electrons have been accepted. The simplification of these equations has been done accepting definite assumptions concerning the parameters of a plasma. The solution has been obtained by applying the expansion in powers of a small parameter of the order of ν/c for electrons, and by a small perturbation of equations in particular order of approximation.