  Spectral evolution of gamma-ray burst pulses assumed to arise from emission
of fireballs is explored. It is found that, due to the curvature effect, the
integrated flux and peak energy are well related by a power law in the decaying
phase of pulses, where the index is about 3, being free of the intrinsic
emission and the Lorentz factor. The spectrum of a pulse in its decaying phase
differs slightly for different intrinsic spectral evolution patterns,
indicating that it is dominated by the curvature effect. In the rising phase,
the integrated flux keeps increasing whilst the peak energy remains unchanged
when the intrinsic emission bears an unchanged spectrum. Within this phase, the
flux decreases with the increasing of the peak energy for a hard-to-soft
intrinsic spectrum, and for a soft-to-hard-to-soft intrinsic spectrum, the flux
generally increases with the increasing of the peak energy. An intrinsic
soft-to-hard-to-soft spectral evolution within a co-moving pulse would give
rise to a pulse-like evolutionary curve for the peak energy.
