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For the purpose of studying the relationship between pulse shape and spectral evolution, we analyzed the time profiles of 45 long (${>}$ 1.5 s), bright (${>}$ 18000 counts s$^{-1}$) gamma-ray bursts detected by the Burst And Transient Source Experiment (BATSE) on the Compton Observatory. The data used are recorded with 64-ms resolution, in 4 energy bands ($\sim$ 25--50, 50--100, 100--300, ${>}$ 300 keV). Pulses in the time profiles were fitted using a pulse model with rise and decay time constants and a peakedness parameter. On average (with a wide variation), 10 pulses are required to represent a burst profile. Considering only the subset of fitted pulses which do not overlap substantially ($\sim$ 20\% of total), we find that most pulse shapes range from symmetric to fast-rise, slow-decay -- with only a small fraction rising more slowly than they decay. Corresponding to this one-sided range in rise-to-decay ratio is a one-sided range in shift of pulse centroid with energy: the lower the rise-to-decay ratio, the farther the centroid at low energy tends to be shifted to later times relative to the centroid at high energy. Most ``separable" pulses in long bursts have widths in the range 200--600 ms (FWHM); pulse centroids shift $\sim$ 0--300 ms from high (${>}$ 300 keV) to low energy (25--50 keV), mostly as a result of pulse narrowing rather than peak shifting, while rise-to-decay ratios decrease from near unity to $\sim$ 0.2.
