Spectra of magnetooptical polaritons in nonlinear magnetogyrotropic medium at presence of magnetostatic field are received. Nonlinear internal ion polarization arisen under the influence of high-frequency electromagnetic field is taken into account. The polariton spectra subjected to strength and direction of the external magnetostatic field are calculated.Dynamics of electromagnetic waves and their spectra or, in other words, polariton spectra in different linear and nonlinear media at presence of magnetostatic field still attract attention of scientists [1,2]. It is connected with applications of the results of researches in magneto-and optoelectronics, and also in various areas of scientific investigations [3]. Depending on the resonant frequency and corresponding response of the medium at external electromagnetic field the polaritons subdivide into the optical and magnetic polaritons, and at partial overlapping of resonant areas they divide into magnetooptical polaritons [4].Optical polaritons are the mixture of photons and phonons. They arise in the frequency range where permittivity of medium differs from unity, and permeability is close to one. The bound states of photons and magnons in magnetic-ordered crystal medium are the magnetic polaritons. Magnetic polaritons arise at the frequencies corresponding to the microwave and terahertz ranges when permittivity of medium is close to unity, and permeability differs from one. Magnetooptical polaritons represent the quasiparticles arising at interrelation of photons, phonons and magnons in the range of frequencies where permittivity and permeability are not equal to unity.The external magnetic field applied to magnetogyrotropic medium changes the response of this medium, and thus it influences on the spectrum of polaritons. Changing the intensity of the external magnetic field it is possible to operate the polariton parameters. The intensity of highfrequency electromagnetic field also influences on the polariton spectrum, in other words, the nonlinear response of medium effects on the spectrum. The purpose of this work is the researching of the dependence of magnetooptical polariton spectra in magnetogyrotropic medium with cubic anisotropy on the direction and strength of external magnetostatic field and from intensity of the electromagnetic field either.The equations of motion of electric charges and magnetic moment. We assume that in a unit cell of the crystal of cubic system positive and negative ions are located. In this case it is possible to introduce the vector of displacement r r R, where vectors r describe the displacement of positive and negative lattices of ions. In macroscopic model of dipole response of the crystal can be described by the equations of charge motion