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 1998 May. 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 GRB 970111, where a low-energy photon depletion with respect to the thin SSM spectrum is observed. A strong and time-variable low-energy cutoff, consistent with absorption effect, is observed during the prompt emission of GRB 980329. 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. We also find that for most of the GRBs in our sample the late emission is consistent with a slow cooling of the shock. Adiabatic shocks appear more likely than radiative shocks. Parameters of the shocks at earliest times have been derived.
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