The new results of cathode surface degradation in muon proportional chambers of CMS after a long-term irradiation with a 90Sr β-source are presented. The data of the complex analysis of the copper foil samples from the cathode are shown. The AFM method revealed the general radiation damage of the copper surface and the dynamics of its change. It is clearly demonstrated that the revealed development of the radiation erosion on the cathode is a result of electron irradiation. Moreover, the nature of erosion and level of the destruction of copper are associated with irradiation intensity. The study of the elemental and phase composition together with the data of structural analysis allowed us to single out the stages of the radiation aging of the copper surface on the cathodes and consider the processes which are at the basis of them.