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The present report is devoed to developing the electromagnetic theory of superconducting structures and its application to the technique of the microwave band. The actuality of the given problem lies in the fact that nowadays there is no any acceptable mathematical methods, by means of which it would be possible to investigate in sufficient details and give designers of the radioelectronic equipment the practical recommendations on solving the internal and exterior boundary value problems, associated with excitation, scattering and propagation of electromagnetic waves on the superconducting (SC) objects of simple and complex shape.