A new method is proposed, which allows the study of generic signatures of c
osmic gamma-ray burst time histories. We average the 64 ms resolution time
profiles of 275 bright bursts detected by BATSE. The profile of each burst
is normalized by the maximum number of counts at the peak of the primary pu
lse, and individual pulses and interpulse valleys are selected from the nor
malized pro files by identical selection criteria. New generic temporal par
ameters are introduced, which characterize the duration and equivalent widt
h of each pulse and the duration of each valley. The histograms of the tota
l equivalent pulse width and summed pulse duration are bimodal. Bimodality
is also seen in the histogram of the mean duration of individual pulses. Bu
rsts from the short and long peaks of these distributions correspond to the
two modes of the Third BATSE Burst Catalog T-50 and T-90 distributions. Th
erefore, these new burst parameters demonstrate that the observed bimodal t
emporal behavior results from properties of the pulsed emission of gamma-ra
y bursts. The long mode of the T-90 histogram includes bursts with from one
to similar to 20 pulses; the logarithmic mean pulse duration is 1.17 +/- 0
.09 s; for the long events with more than one pulse, the logarithmic mean v
alley duration is 1.28 +/- 0.15 s. Bursts of the short mode of T-90 are mai
nly single-pulse events, and the logarithmic mean pulse duration is much sm
aller, 0.20 +/- 0.01 s. For multipulse bursts of the T-90 long mode, margin
al correlations were found between the parameters of the pulses and valleys
and the number of pulses. The basic signatures of the evolution of pulses
and valleys along the time course of bursts are examined. Conclusions are d
rawn concerning the physics of gamma-ray emission by taking into account th
ese signatures.