  We describe our attempt to determine if gamma-ray burst (GRB) and afterglow
emissions could both arise in external shocks for simple GRBs--bursts
consisting of just a few peaks in their lightcurves. We calculate peak flux and
peak frequency during the gamma-ray burst for ten well observed bursts using
the same set of parameters that are determined from modeling afterglow
emissions. We find the gamma-ray emission properties for 970508 (which had a
single peak lightcurve) fit nicely with the extrapolation of its afterglow
data, and therefore this burst was likely produced in the external shock. One
can explain two other bursts in this sample as forward shock synchrotron
emission provided that the magnetic field parameter during the burst is close
to equipartition, and larger by a factor of 100 than the afterglow value at ~1
day. The remaining seven bursts cannot be explained in the external shock model
even if we allow the energy fraction in electrons and magnetic field and the
density of the surrounding medium to take on any physically permitted value;
the peak of the spectrum is above the cooling frequency, therefore the peak
flux is independent of the latter of these two parameters, and is too small by
about an order of magnitude than the observed values. We have also considered
inverse-Compton scattering in forward and reverse shock regions and find that
it can explain the gamma-ray emission for a few bursts, but requires the
density to be 1--2 orders of magnitude larger than a typical Wolf-Rayet star
wind and much larger than permitted by late afterglow observations. [Abridged]
