1 Introduction

The BeppoSAX discovery of X-ray afterglows of Gamma-Ray Bursts (GRBs) has solved a great mystery about these events but many questions are still open about the origin of the GRB primary events and afterglows and their correlation. BeppoSAX offers the possibility to perform in a broad energy band (2-700 keV) spectral studies of the primary events and follow in the 0.1-10 keV range the light curve and the spectrum of the GRB afterglow down to $10^{-13}\, {\rm erg/(cm^2 \, s)}$.

We report here on some relevant results of an investigation, performed on a sample of GRBs observed with both the Wide Field Cameras (WFCs, 2-26 keV, Jager et al. 1997) and the Gamma-ray Burst Monitor (GRBM, 40-700 keV, Frontera et al. 1997; Feroci et al. 1997), devoted to study: (a) the evolution of the GRB spectral properties during the burst and their consistency with the synchrotron shock model (e.g., Katz 1994; Tavani 1996; Sari et al. 1998); (b) the correlation between energetics in GRBs and that in the associated X-ray afterglows; (c) the correlation between spectral properties of GRB events and fading law of the corresponding X-ray afterglows; (d) the hydrodynamical evolution of a fireball shock according to the model by Sari et al. (1998).