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It is known that parasitic resonances may occur in the noncontacting plunger of a coaxial-line resonator, when the wavelength is less than the circumference of the outer gap. When it is not possible to select inner and outer diameters such that the parasitic resonances occur at wavelengths outside of the tuning range, these resonances must be controlled by cutting grooves or slots in the plunger. This paper develops a theory of the resonances in a slotted plunger based upon a loaded-transmission-ring model. The wavelengths at which the parasitic resonances occur as calculated from this model are found to be in satisfactory agreement with experimental measurements made upon a typical plunger. It is concluded that ordinarily an odd number of slots is preferable to an even number, and that the parasitic resonances are more readily controlled in the Z-type than in the British S-type plunger.