Abstract:Background. The aim of this work is to study the properties of the spectrum of the problem of propagation of electromagnetic waves of an open circular waveguide with an inhomogeneous chiral layer. Material and methods. To find a solution, the method of operator-functions is used. Results. Spectral properties of the problem of normal waves of an open circular waveguide with an inhomogeneous chiral layer are studied. Conclusions. The proposed approach can be applied to study surface waves of regular inhomogeneous open wave-carrying structures with chiral media.