We present the results of searches for periodic pulsations in gamma-ra
y bursts detected by the Burst and Transient Source Experiment (BATSE)
aboard the Compton Gamma Ray Observatory. A total of 20 bright bursts
are examined. The durations of the time-tagged event (TTE) data used
a range from 0.065 to 1.048 s. These data cover either the onset of a
very bright burst or the whole short burst. The photon arrival data ar
e time-tagged with a time resolution of 2 mu s. We examined various en
ergy channels and time segments in the data for pulsations using fast
Fourier transform. The periods searched cover the range 0.016-33.3 ms.
We find no significant evidence for periodic pulsations in the above
range, and the upper limits for the pulsations are presented in terms
of statistical probabilities and pulsed fractional amplitudes.