  One of the most impressive recent discovery of SWIFT is the evidence that
X-ray flares occurring during the GRB afterglows are quite common, being
observed in roughly 50% of the afterglows. These X-ray flares range fluences
comparable with the GRB prompt emission and could be also repetitive. Several
pictures have been proposed on their origin and among them the most accepted
regards the internal shock scenario, interpreting the X-ray flares as late time
activity of the GRB central engine. We propose to describe the spectral shape
of the X-ray flares adopting the same physical model recently used to interpret
the GRB prompt emission: the log-parabolic function. In particular, we show
that their spectral energy distribution (SED) is remarkably curved, while no
significant curvature appears in the underlying X-ray afterglow emission. In
addition, the log-parabolic function is statistically favored with respect to
other proposed spectral models. By using a time resolved spectral analysis, we
show the evolution of the peak energy and the curvature parameters of the SED
during the X-ray flares in two of the brightest GRBs afterglows observed by
SWIFT. We found that in the X-ray flares there is an anti-correlation between
the peak energy and the curvature, as expected in a stochastic acceleration
scenario.
