In this chapter, the authors deal with linear relations between AC components of magnetization and magnetic field, which were found by solving the linearized equations of motion. The Landau–Lifshitz equation can be solved rigorously, at arbitrary amplitudes of the AC field, only in a few particular cases. The simplest case is the magnetization precession in the AC field with circular polarization. The instability in the nonlinear motion of the magnetization at the high power levels can be caused not only by the shape anisotropy of the sample but also by other kinds of anisotropy (e.g., by the magnetocrystalline anisotropy) that lead to the dependence of the eigenfrequency on the ac magnetization amplitude. Such dependence and, hence, the instability can arise also because of the change of the anisotropy constants due to the heating of the sample by the ac field.