  We report on the temporal behavior of the high-energy power law continuum
component of gamma-ray burst spectra with data obtained by the Burst and
Transient Source Experiment. We have selected 126 high fluence and high flux
bursts from the beginning of the mission up until the present. Much of the data
were obtained with the Large Area Detectors, which have nearly all-sky
coverage, excellent sensitivity over two decades of energy and moderate energy
resolution, ideal for continuum spectra studies of a large sample of bursts at
high time resolution. At least 8 spectra from each burst were fitted with a
spectral form that consisted of a low-energy power law, a spectral break at
middle energies and a high-energy continuum. In most bursts (122), the
high-energy continuum was consistent with a power law. The evolution of the
fitted high-energy power-law index over the selected spectra for each burst is
inconsistent with a constant for 34% of the total sample. The sample
distribution of the average value for the index from each burst is fairly
narrow, centered on -2.12. A linear trend in time is ruled out for only 20% of
the bursts, with hard-to-soft evolution dominating the sample (100 events). The
distribution for the total change in the power-law index over the duration of a
burst peaks at the value -0.37, and is characterized by a median absolute
deviation of 0.39, arguing that a single physical process is involved. We
present analyses of the correlation of the power-law index with time, burst
intensity and low-energy time evolution. In general, we confirm the general
hard-to-soft spectral evolution observed in the low-energy component of the
continuum, while presenting evidence that this evolution is different in nature
from that of the rest of the continuum.
