The detection of primary cosmic ray electrons with energies above 1 Te
V implies the existence of a nearby, r less than or equal to 100 pc, a
nd relatively young, t less than or equal to 10(5) yr, source(s) of ac
celerated electrons. Therefore a correct treatment of the formation of
the spectra of electrons during their propagation in the interstellar
medium requires a separate consideration of the contribution of one (
or a few) nearby source(s) from the contribution of distant (R greater
than or equal to 1 kpc) sources. To implement this approach, the prob
lem of energy-dependent diffusive propagation of relativistic particle
s from a single source is considered, and the analytical solution to t
he diffusion equation in the general case of arbitrary energy losses a
nd injection spectrum of primary particles is found. We show that in t
he framework; of the proposed two-component approach, i.e., separating
the contribution of the local (discrete) source(s) from the contribut
ion of distant sources, it is possible to explain all the locally obse
rved features of the energy spectrum of cosmic ray electrons from sub-
GeV to TeV energies. In addition, assuming that the local source produ
ces electrons and positrons in equal amounts, the model allows us to e
xplain also the reported increase of the positron content in the flux
above 10 GeV.