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The spectral theory of open waveguide structures is successfully employed over a period of years for studying electromagnetic properties of extended structures of waveguide type (waveguide broadening of finite length, finite length dielectric bifurcation of a waveguide etc.). Our work presents some results of applying the spectral theory to the analysis of waveguide unhomogeneities with small longitudinal dimensions, namely multiple aperture rectangular irises in a rectangular waveguide. Rejection frequency response is the salient feature of such irises if their cross-section contains at least two slots of different geometry. A number of works were devoted to studying frequency responses of rejection multiple aperture irises. A tool of their studying was or the circuit theory [1] or the diffraction theory [2]. In our previous works [3, 4] we have established, in particular, that the number of total transmission responses on the iris frequency response are coincident with the number of the slots having different geometry. Dimensions of these apertures define the location and quality factor of the total transmission resonances. However the reason of forming such a frequency response is not revealed yet. Employment of the spectral theory can give an answer for this question.