Abstract
We study the production of cosmic rays (CRs) in supernova remnants (SNRs), including the production of electron and positron CR components. This combines for the first time nuclear collisions inside CR sources and in the diffuse interstellar medium leading to the creation of electrons and positrons, as well as their reacceleration, with the injection and subsequent acceleration of suprathermal protons and electrons from the postshock thermal pool. Selfconsistent CR spectra are calculated on the basis of the nonlinear kinetic model. It is shown that reacceleration of positrons created in SNR and ISM produces a considerable effect at energies above 10 GeV, making its energy spectrum substantially flatter than the spectrum created in ISM. Calculated electron and positron spectra are in the satisfactory agreement with the existing measurements.