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A substantial control of dispersion features of the hybrid EH01 and HE11 modes of a circular waveguide which is completely filled by a longitudinally magnetized composite finely-stratified ferrite-semiconductor structure is discussed. A relation between the resonant conditions of such a composite gyroelectromagnetic filling of the circular waveguide and dispersion features of the supported modes are studied. Three distinct frequency bands with the singlemode operation under normal as well as anomalous dispersion conditions of the EH01 mode are identified by solving an optimization problem with respect to the filling factors of the composite medium. The possibility of achieving isolated propagation of the HE11 mode is revealed.