Abstract: In this paper the propagation of cosmic ray e ectrons with energy larger than 10¹²eV is investigated.Our theoretical calculations show shat the effects of resonant scattering caused by the interstellar hydromagntic waves on the propagation of cosmic ray electrons are very important.On the basis of it the solution of the kinetic equation of cosmic ray electrons leads to the following conclusions:1)Due to the interstellar scattering, the maximum flux of cosmic ray electrons coming from the supernova surces which are in a distance less than 1 kpc from us has not arrived in the earth yet.So the flux of cosmic ray electrons in the neighbourhood of the earth is still in the ascending stage.2)In TeVenergy region, a "dropping phenomena" of the electron energy spectrum is expected.3)The high energy y-ray source observed by SAS-2 may be produced by inverse compton effect through the interaction of cosmic ray electrons with the interatellar radiation fields.Asupport to this suggestion comes from the fact that the dimension of the y-ray source is in agreement with that of cosmic ray electron cloud characterized by the gaussian half width W_Gⁱ≌(4ξti)^1/2√ln2 drived in this paper.