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Subject and Purpose. The research focuses on how the resonance frequencies, the Q-factor of resonances, and the polarization plane rotation ability are influenced by the topology of individual components of a planar-chiral double-layer object consisting of a pair of conjugated irises having rectangular slots and accommodated in a circular waveguide. Methods and Methodology. All the numerical results are obtained by the mode-matching technique (MMT) and the transverse resonance method on the basis of our own proprietary MWD-03 software package. Results. By the waveguide example, it has been shown that the internal structure of individual components and dihedral symmetry of the conjugated bilayer allow all the conclusions of the spectral theory (theory of eigen-oscillations) to be carried over to all the objects of the type. On the other hand, these objects behave as symmetric two-port waveguide components with conventionally "symmetric" and "antisymmetric" eigen-oscillations. The mutual coupling of these eigen-oscillations depends on the bilayer parameters. Where the frequencies of these eigen-oscillations are close enough, the polarization plane rotation and the transmission bandwidth reach their highest. It has been demonstrated that as a slot number increases, the resonance frequency decreases. The theoretical results have been confirmed by the measurements at the X range of frequencies for pairs of conjugated irises with various numbers of rectangular slots. Conclusions. A pair of conjugated chiral irises can rotate the polarization plane. The iris topology, iris spacing, and the mutual rotation angle alter resonance frequencies. The resonance frequencies can be reduced by increasing the rectangular slot length and/or slot number. Even though they have not longitudinal symmetry, such objects have properties of two-port waveguide components. In particular, the phase shift of their reflection and transmission coefficients is modulo 90°. Besides, a possibility exists to divide eigen-oscillations into conventionally "symmetric" and "antisymmetric" based on the proximity of their fields to those whose type of symmetry is known before- hand. This makes it possible to approximate the reflection and transmission coefficients through corresponding eigenfrequencies.