The spectral theory is used to explain the enhanced transmission phenomenon. Eigenoscillations of corresponding waveguide and periodic open resonators have been studied. Their influence on frequency response is demonstrated for various structures. It has been found that the origin of this recently discovered effect is in the existence of the eigenoscillations of the interface between the free half-space and the metal half-space perforated with double-periodic set of channels or the eigenoscillations of the waveguide plane junction.