We have analyzed the evolution of the spectral hardness parameter, E-pk (th
e maximum of the nu F-nu spectrum) as a function of fluence in gamma-ray bu
rsts. We fit 41 pulses within 26 bursts with the trend reported by Liang &
Kargatis (1996) which found that E-pk decays exponentially with respect to
photon fluence Phi(t). We also fit these pulses with a slight modification
of this trend, where E-pk decays linearly with energy fluence. In both case
s, we found the set of 41 pulses to be consistent with the trend.