  Employing a sample presented by Kaneko et al. (2006) and Kocevski et al.
(2003), we select 42 individual tracking pulses (here we defined tracking as
the cases in which the hardness follows the same pattern as the flux or count
rate time profile) within 36 Gamma-ray Bursts (GRBs) containing 527
time-resolved spectra and investigate the spectral hardness, $E_{peak}$ (where
$E_{peak}$ is the maximum of the $\nu F_{\nu}$ spectrum), evolutionary
characteristics. The evolution of these pulses follow soft-to-hard-to-soft (the
phase of soft-to-hard and hard-to-soft are denoted by rise phase and decay
phase, respectively) with time. It is found that the overall characteristics of
$E_{peak}$ of our selected sample are: 1) the $E_{peak}$ evolution in the rise
phase always start on the high state (the values of $E_{peak}$ are always
higher than 50 keV); 2) the spectra of rise phase clearly start at higher
energy (the median of $E_{peak}$ are about 300 keV), whereas the spectra of
decay phase end at much lower energy (the median of $E_{peak}$ are about 200
keV); 3) the spectra of rise phase are harder than that of the decay phase and
the duration of rise phase are much shorter than that of decay phase as well.
In other words, for a complete pulse the initial $E_{peak}$ is higher than the
final $E_{peak}$ and the duration of initial phase (rise phase) are much
shorter than the final phase (decay phase). This results are in good agreement
with the predictions of Lu et al. (2007) and current popular view on the
production of GRBs. We argue that the spectral evolution of tracking pulses may
be relate to both of kinematic and dynamic process even if we currently can not
provide further evidences to distinguish which one is dominant. Moreover, our
statistical results give some witnesses to constrain the current GRB model.
