A statistical study on the light curves of all the short Gamma-Ray Bursts detected with the Gamma Ray Burst Monitor (GRBM) aboard BeppoSAX is reported. Evidence for a very weak and long duration component associated with these events in the two 1 s counters of the GRBM (40-700 keV and >100 keV) is found. It starts a few tens of seconds before the burst and continues for about 30 s after the burst. The overall hardness of this component is comparable with that of the event itself. The detection of a signal before the onset time and the similar hardness are consistent with an interpretation of the long duration component in terms of prompt emission associated with short GRBs.
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