[en] The problem of the necessity of considering non-linear effects in geomagnetic pulsations, in connection with the study of a new class of instabilities of magnetospheric plasma, related to the swing of the Alfven oscillations is discussed. Mechanisms of these instabilities are connected with the compressibility of plasma conditioned both by the curvature of lines of force of the geomagnetic field and the effect of the finite Larmor radius of ions. The consideration of pulsations is necessitated by the fact that in some cases the amplitude of geomagnetic pulsations is comparable with the range of pulsations of the external magnetic field. An example of the dependence of the transversal pressure of Psub(tr)plasma on the coordinate x and the distribution of the Alfven waves connected with it is discussed. It is shown that under the observed dependence of Psub(tr) on x the accumulation of the energy density of the Alfven oscillations occurs in the areas of the minimum pressure of hot plasma, their amplitude in these areas can reach high values. Such distribution of the Alfven oscillations is typical for geomagnetic pulsations of the Pc-3 type and corresponds to the middle-latitude and high-latitude maximum in the Pc-3 oscilations