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A new algorithm is utilized to examine the phase and attenuation constants of open dissipative epsilon- and (or) mu-gyrotropic rod waveguides. Our algorithm allows analyzing the waveguides made of materials having very high losses. The dispersion characteristics of p-Ge with a waveguide of two component hole charge carders are calculated when the ratio of heavy hole concentration in the material is equal to 5%, 50% and 95% of the total free carrier concentration. The effective mass of p-Ge heavy and light holes are 0.279me and 0.043me respectively. The dispersion characteristics of the main and eight higher modes are presented in the paper. The transformation of higher hybrid modes at some heavy hole concentrations can be noticed. Waveguide broad bandwidth can be considerably extended due to the fact that the losses of higher modes are larger in comparison to those of the main mode at certain heavy hole concentration. [ABSTRACT FROM AUTHOR]