The observations of radio emission from supernova remnant SNR 1987A ca
n be accounted for on the basis of diffusive shock acceleration of ele
ctrons by the supernova blast wave. However, with this interpretation
the observed spectral index implies that the compression ratio of the
gas subshock is roughly 2.7 rather than the value of 4 expected of a s
trong shock front. We propose that in SNR 1987A, ions also undergo dif
fusive acceleration at the shock, a process that is likely to be rapid
. Unlike the electron population, the accelerated ions can have an imp
ortant effect on the gasdynamics. We calculate this coupled gas and en
ergetic particle dynamics on the basis of the two-fluid model, in whic
h the accelerated ions provide an additional component to the total pr
essure acting on the fluid. By accelerating and possibly heating the u
pstream plasma, the initially strong shock is modified and a weaker su
bshock with an upstream precursor results. The electrons behave as tes
t particles. They are accelerated at the evolving subshock, escape dow
nstream, and emit synchrotron radiation in the swept up magnetic field
. Two models are considered for the surroundings of the progenitor: th
at of a freely expanding wind of number density n proportional to r(-2
) and that of a wind confirmed by a shell of denser material, creating
a stagnation zone of roughly constant density beyond the standing sho
ck which terminates the free wind, We model the observed radio light c
urves and the relatively steep spectrum of SNR 1987A using similar val
ues for the ion acceleration parameters to those used in models of cos
mic-ray acceleration in older SNRs, which can also contain high Mach n
umber shocks, and find a good fit for the case in which the terminatio
n shock is located at about 2 x 10(15) m from the progenitor.