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Extraordinary dispersion features of a circular waveguide filled by a longitudinally magnetized composite gyroelectromagnetic medium are studied. The composite medium is considered to be constructed by juxtaposition together of magnetic and semiconductor layers providing all characteristic dimensions of the resulting multilayered system are much smaller than the wavelength in the corresponding part of the composite medium. The waveguide dispersion equation and its eigenmodes are derived. The mode classification is made in a standard manner so that the guided modes are sorted into a class of hybrid HE and EH waves in terms of their unique dispersion characteristics. The numerical results are obtained in the band near the frequencies of corresponding resonances in constitutive materials of the composite medium, and they show that the modes behaviors become to be quite diverse due to manifestation of a strong combined geometrical and material dispersion related to the waveguide parameters and gyroelectromagnetic filling, respectively.