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Abstract: In this paper, from the generalized telegraph equations waveguide cavities with slowly varying cross-section are studied. The mode resonant frequencies and the quality factors (Q s) of these cavities and the field distributions are found when the boundary conditions at the ends and at discontinuities are given. Honp modes in an opend circu-lar waveguide cavity with slowly varying cross-section are studied in some details, espe-cially the diffractive losses of these modes at the opened ends of the cavity are obtained. Finally, two sets of universal curves for resonant frequencies and Q's are given fro the double conic opened cavities which are most frequently used in practice. Some results of experiments prove their use rather reliable.