Gamma-ray burst time histories often consist of many peaks. These peak
s tend to be narrower at higher energy. If gamma-ray bursts are cosmol
ogical, the energy dependence of gamma-ray burst timescales must be un
derstood in order to correct the timescale dependence due to the expan
sion of the universe. By using the average autocorrelation function an
d the average pulse width, we show that the narrowing with energy foll
ows, quite well, a power law. The power-law index is similar to-0.4. T
his is the first quantitative relationship between temporal and spectr
al structure in gamma-ray bursts. It is unclear what physics causes th
is relationship. The average autocorrelation has a universal shape suc
h that one energy range scales linearly with time into all other energ
y ranges. This shape is approximately the sum of two exponentials.