Nonlinear Kinetic Theory of Cosmic-ray Acceleration in Supernova Remnants

A review of kinetic nonlinear theory for cosmic-ray (CR) acceleration and subsequent -ray production due to CR nuclear component in supernova remnants (SNRs) is presented. The correspondence of the expected spectrum and composition of CRs produced inside SNRs in the Galaxy with the experimental data is discussed. Possible explanations of negative results in searching high energy -ray emission from nearby SNRs are analyzed.