The inadequacy of Lie´nard-Wiechert potentials is demonstrated as one of the examples related to the inconsistency of the conventional classical electrodynamics. The insufficiency of the Faraday-Maxwell concept to describe the whole electromagnetic phenomenon and the incompleteness of a set of solutions of Maxwell equations are discussed and mathematically proved. Reasons for the introduction of the so-called ‘‘electrodynamics dualism concept’’ ~simultaneous coexistence of instantaneous Newton long-range and Faraday- Maxwell short-range interactions! have been displayed. It is strictly shown that the new concept presents itself as the direct consequence of the complete set of Maxwell equations and makes it possible to consider classical electrodynamics as a self-consistent and complete theory, devoid of inward contradictions. In the framework of the new approach, all main concepts of classical electrodynamics are reconsidered. In particular, a limited class of motion is revealed when accelerated charges do not radiate electromagnetic field.Producción Científica de la Universidad Autónoma de Zacatecas UAZ