We consider in this paper the effect of synchrotron self-Compton process on
X-ray afterglows of gamma-ray bursts. We find that for a wide range of
parameter values, especially for the standard values which imply the energy in
the electrons behind the afterglow shock is tens times as that in the magnetic
field, the electron cooling is dominated by Compton cooling rather than
synchrotron one. This leads to a different evolution of cooling frequency in
the synchrotron emission component, and hence a different (flatter) light curve
slope in the X-ray range. This effect should be taken into account when
estimating the afterglow parameters by X-ray observational data. For somewhat
higher ambient density, the synchrotron self-Compton emission may be directly
detected in X-ray range, showing varying spectral slopes and a quite steep
light curve slope.Comment: 6 pages, 3 figures, accepted to MNRA