  We report evidence that the asymptotic low-energy power law slope alpha
(below the spectral break) of BATSE gamma-ray burst photon spectra evolves with
time rather than remaining constant. We find a high degree of positive
correlation exists between the time-resolved spectral break energy E_pk and
alpha. In samples of 18 "hard-to-soft" and 12 "tracking" pulses, evolution of
alpha was found to correlate with that of the spectral break energy E_pk at the
99.7% and 98% confidence levels respectively. We also find that in the flux
rise phase of "hard-to-soft" pulses, the mean value of alpha is often positive
and in some bursts the maximum value of alpha is consistent with a value > +1.
BATSE burst 3B 910927, for example, has a alpha_max equal to 1.6 +/- 0.3. These
findings challenge GRB spectral models in which alpha must be negative of
remain constant.
