  A nonlinear kinetic theory of cosmic ray (CR) acceleration in supernova
remnants is employed to investigate the properties of the remnant SN 1987A. It
is shown that a large downstream magnetic field ~10 mG is required to fit the
existing observational data. Such a strong field together with the strong shock
modification due to CR backreaction provides the steep and concave
radioemission spectrum and considerable synchrotron cooling of high energy
electrons which diminish their X-ray synchrotron flux below the observed
Chandra flux which has to be considered as an upper limit for nonthermal X-ray
emission. The expected gamma-ray energy flux at TeV-energies at the current
epoch is 2x10^{-13} erg/(cm^2 s).
