In this work some problems of dynamics of magnetospherical charged particles of high energies (1 –1000 M_eV) are considered. The coefficients of a pitch-angular and radial diffusion of protons and electrons in a dipole magnetic field are defined. The calculations were grounded on the basic kinetic equation with use of a method by G. M. Zaslavsky [1]. Our calculations were based on the results of the modern theory of nonlinear oscillations in dynamic systems [1, 2]. The aim of the work was to define a role of the mechanism of the breaking down of the first adiabatic invariant in shaping pitch-angular distribution of particles in the magnetosphere. It is shown, that the considered mechanism of scattering reduces in a strong pitch-angular diffusion of protons and heavier ions, while the beams of polar electrons are very stable, can be long-lived in time and oscillate between points of reflection, which are in the polar zones. On the basis of the obtained results it is possible to explain and to interpret origin and stability of auroras, and also radio-frequency radiation from magneto-spheres of planets as secondary effect of a stability of polar electron beams.