  We investigated the spectral evolution in the 2--700 keV energy band of
Gamma-Ray Bursts (GRBs) detected by the Gamma-Ray Burst Monitor (GRBM) and
localized with the Wide Field Cameras (WFCs) aboard the BeppoSAX satellite
before May 1998. Most of them have been followed-up with the Narrow Field
Instruments aboard the same satellite. In the light of these results we discuss
open issues on the GRB phenomenon. We find that the optically thin synchrotron
shock model (SSM) provides an acceptable representation of most of the
time-resolved GRB spectra extending down to 2 keV, except in the initial phases
of several bursts and during the whole duration of the quite strong GRB970111,
where a low-energy photon depletion with respect to the thin SSM spectrum is
observed. We find that the X-ray afterglow starts at about 50% of the GRB
duration, and that its fluence, as computed from the WFC light curve, is
consistent with the decay law found from the afterglow NFI observations. We
also investigate the hydrodynamical evolution of the GRB in our sample and
their associated afterglow, when it was detected. We find that the photon index
of the latest spectrum of the GRB prompt emission is correlated with the index
of the afterglow fading law, when available, as expected on the basis of an
external shock of a relativistic fireball.
