The cosmological origin of gamma -ray bursts (GRB's) is now commonly accept
ed and, according to several models for the central engine, GRB sources sho
uld also emit at the same time gravitational wave bursts (GWB's). We have p
erformed two correlation searches between the data of the resonant gravitat
ional wave detector AURIGA and GRB arrival times collected in the BATSE 4B
catalogue. No correlation was found and an upper limit h(RMS)less than or e
qual to 1.5x10(-18) on the averaged amplitude of gravitational waves associ
ated with gamma -ray bursts has been set for the first time.