Circular multilayered waveguides are often used as parts of various devices of the microwave and EHF ranges. The layered structure of the filling of a waveguide allows more flexibility to configure and optimize the parameters of the device. In a waveguide with inhomogeneous cross section, one can obtain different cutoff frequencies of modes than the cutoff frequency of the hollow waveguide. This article describes a new method of obtaining the dispersion characteristics of radially inhomogeneous circular waveguides based on the use of conditions of the transverse resonance in equivalent radial transmission lines. The proposed method is effective for the preparation of the dispersion equations, as it uses the theory of microwave circuits and recursive expressions instead of directly solving the system of equations that are boundary conditions between layers.