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Analytical hybrid-mode dispersion relations of a lossy coaxial waveguide were rigorously analyzed using a mode-matching technique. In order to model a practical coaxial line with inevitable losses, we adopted an all-dielectric coaxial waveguide surrounded by the perfect electric conductor (PEC) boundary. The rigorous dispersion characteristics of the TM01, TE01, and EH11 modes were investigated for lossy coaxial waveguides filled with different electrical conductivities. Based on the exact solutions, approximate but accurate dispersion equations were proposed for the TM0p, TE0p, EHmp, and HEmp modes in order to estimate and compare the behaviors of complex propagation constants in the microwave and visible spectra. [ABSTRACT FROM AUTHOR]