  This paper presents the results of the observations of the detectors
participating in the International Gravitational Event Collaboration (IGEC)
from 1997 to 2000 and reviews the data analysis methods. The analysis is
designed to search for coincident excitations in multiple detectors. The data
set analysed in this article covers a longer period and is more complete than
that given in previous reports. The current analysis is more accurate for
determining the false dismissal probability for a time coincidence search and
it optimizes the search with respect to a target amplitude and direction of the
signal. The statistics of the accidental coincidences agrees with the model
used for drawing the results. The observations of this IGEC search are
consistent with no detection of gravitational wave burst events. A new
conservative upper limit has been set on the rate of gravitational wave bursts
with Fourier component H > 2 10^{-21}Hz^{-1}, both for searches with and
without a filter for the Galactic Center direction. This study confirms that
the false alarm rate of the observation can be negligible when at least three
detectors are operating simultaneously.
