In the context of polaritons in a ferrite-semiconductor structure which is influenced by an external static magnetic field, the gyrotropic-nihility can be identified from the dispersion equation related to bulk polaritons as a particular extreme state, at which the longitudinal component of the corresponding constitutive tensor and bulk constant simultaneously acquire zero. Near the frequency of the gyrotropic-nihility state, the conditions of branches merging of bulk polaritons, as well as an anomalous dispersion of bulk and surface polaritons are found and discussed.