  A GRB afterglow has been commonly thought to be due to continuous
deceleration of a postburst fireball. Many analytical models have made
simplifications for deceleration dynamics of the fireball and its radiation
property, although they are successful at explaining the overall features of
the observed afterglows. We here propose a model for a GRB afterglow in which
the evolution of a postburst fireball is in an intermediate case between the
adiabatic and highly radiative expansion. In our model, the afterglow is both
due to the contribution of the adiabatic electrons behind the external
blastwave of the fireball and due to the contribution of the radiative
electrons. In addition, this model can describe evolution of the fireball from
the extremely relativistic phase to the non-relativistic phase. Our
calculations show that the fireball will go to the adiabatic expansion phase
after about a day if the accelerated electrons are assumed to occupy the total
internal energy. In all cases considered, the fireball will go to the mildly
relativistic phase about $10^4$ seconds later, and to the non-relativistic
phase after several days. These results imply that the relativistic adiabatic
model cannot describe the deceleration dynamics of the several-days-later
fireball. The comparison of the calculated light curves with the observed
results at late times may imply the presence of impulsive events or energy
injection with much longer durations.
