A new method is proposed, which allows the study of generic signatures of cosmic 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 pulse, and individual pulses and interpulse valleys are selected from the normalized profiles by identical selection criteria. New generic temporal parameters are introduced, which characterize the duration and equivalent width of each pulse and the duration of each valley. The histograms of the total equivalent pulse width and summed pulse duration are bimodal. Bimodality is also seen in the histogram of the mean duration of individual pulses. Bursts from the short and long peaks of these distributions correspond to the two modes of the Third BATSE Burst Catalog T(sub 50) and T(sub 90) distributions. Therefore, these new burst parameters demonstrate that the observed bimodal temporal behavior results from properties of the pulsed emission of gamma-ray bursts. The long mode of the T(sub 90) histogram includes bursts with from one to approximately 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 valley duration is 1.28 +/- 0.15 S. Bursts of the short mode of T(sub 90) are mainly single-pulse events, and the logarithmic mean pulse duration is much smaller, 0.20 +/- 0.01 s. For multipulse bursts of the T(sub 90) long mode, marginal 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 drawn concerning the physics of gamma-ray emission by taking into account these signatures.