The dynamics of propagation of periodic electromagnetic waves and the related electric current in bundles of carbon nanotubes is studied. The study is based on an analysis of coupled equations for the classical electron distribution function in carbon nanotubes and the Maxwell equations for an electromagnetic field. An effective equation is obtained to describe the electromagnetic-field dynamics. Periodic changes are revealed in the shape of the electromagnetic wave propagating in a carbon medium. This effect is considered to be related to energy exchange between periodic oscillations having different periods. Certain regions of the current passing through carbon nanotubes form a periodic domain structure. The results of numerical calculations allow this effect to be analyzed as a function of the problem parameters.