  A nonlinear kinetic theory of cosmic ray (CR) acceleration in supernova
remnants is employed to re-examine the nonthermal properties of the remnant of
SN 1987A for an extended evolutionary period of 5--100 yr. It is shown that an
efficient production of nuclear CRs leads to a strong modification of the outer
supernova remnant shock and to a large downstream magnetic field
$B_\mathrm{d}\approx 20$ mG. The shock modification and the strong field are
required to yield the steep radio emission spectrum observed, as well as to
considerable synchrotron cooling of high energy electrons which diminishes
their X-ray synchrotron flux. These features are also consistent with the
existing X-ray observations. The expected \gr energy flux at TeV-energies at
the current epoch is nearly $\epsilon_{\gamma}F_{\gamma}\approx 4\times
10^{-13}$ erg cm$^2$s$^{-1}$ under reasonable assumptions about the overall
magnetic field topology and the turbulent perturbations of this field. The
general nonthermal strength of the source is expected to increase roughly by a
factor of two over the next 15 to 20 yrs; thereafter it should decrease with
time in a secular form.
