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Topological transitions of isofrequency surfaces are studied in the long-wavelength approximation for a biaxial gyroelectromagnetic medium influenced by an external static magnetic field. For the lossless case, the topological transitions from a closed ellipsoid to open Type I and Type II hyperboloids as well as a bi-hyperboloid are demonstrated. Conditions for critical points where the topological transitions occur are found out. It is revealed that material losses in the constituents of the composite medium strongly influence the dispersion of the extraordinary waves. In particular, the loss-induced topological transitions take place for these waves. It is shown that the loss-induced topological transitions from a Type I hyperboloid to a bi-hyperboloid appear in the frequency band where the real part of at least one principal component of the anisotropic constitutive parameter (permittivity or permeability tensor) is close to zero, whereas its imaginary part is high.