  We find and study a variety of the spectral-temporal behavior during the
decay phase of the light curve of long and bright pulse structures in gamma-ray
bursts. It was earlier found that for about half of these decays, the
instantaneous photon flux is consistent with a power law in time, where the
photon flux $\propto$ 1/time. This decay behavior is a consequence of the
validity of both a power law hardness-intensity correlation (HIC) and an
exponential hardness-fluence correlation (HFC). Beside this behavior, we find
that the other cases approximately behave as 1/(time)$^3$. For a few of these
latter decays, the two correlations (HIC and HFC) are constrained and found to
be consistent with the light curve behavior. For these cases, the HIC is still
a power law while the HFC is described by a generalized function. We study and
describe these behaviors analytically and examine actual burst data from the
complete catalog of the BATSE on the CGRO.
