  We report the initial results from a search for bursts of gravitational
radiation by a network of five cryogenic resonant detectors during 1997 and
1998. This is the first significant search with more than two detectors
observing simultaneously. No gravitational wave burst was detected. The false
alarm rate was lower than 1 per 10^4 years when three or more detectors were
operating simultaneously. The typical threshold was H ~ 4 10^-21 Hz^-1 on the
Fourier component at ~ 10^3 Hz of the gravitational wave strain amplitude. New
upper limits for amplitude and rate of g.w. bursts have been set.
