  We investigate the dynamics and radiation from a relativistic blast-wave
which decelerates as it sweeps up ambient matter. The bulk kinetic energy of
the blast-wave shell is converted into internal energy by the process of
accreting external matter. If it takes the form of non-thermal electrons and
magnetic fields, then this internal energy will be emitted as synchrotron and
synchrotron self-Compton radiation. We perform analytic and numerical
calculations for the deceleration and radiative processes and present
time-resolved spectra throughout the evolution of the blast-wave. We also
examine the dependence of the burst spectra and light curves on various
parameters describing the magnetic field and non-thermal electron
distributions. We find that for bursts such as GRB~910503, GRB~910601 and
GRB~910814, the spectral shapes of the prompt gamma-ray emission at the peaks
in $\nu F_\nu$ strongly constrain the magnetic fields in these bursts to be
well below ($\la 10^{-2}$) the equipartition values. These calculations are
also considered in the context of the afterglow emission from the recently
detected gamma-ray burst counterparts.
