The cutoff characteristics of dielectric-filled circular holes embedded in a dispersive plasmonic medium are investigated. Since two distinctive operating modes, surface plasmon polariton and circular waveguide modes, can exist in the slow and fast wave regions, respectively, the cutoff characteristics for each are separately investigated for linear and radial polarizations of the guided fields. As a result, the cutoff wavelengths for the linear and radial polarizations with very small subwavelength hole radii are found to be limited by the plasma resonance wavelength and plasma wavelength, which in turn are dependent and independent, respectively, of the dielectric constant of the dielectric filler material.