  We propose to explain the recent observations of GRB early X-ray afterglows
with SWIFT by the dissipation of energy in the reverse shock which crosses the
ejecta as it is decelerated by the burst environment. We compute the evolution
of the dissipated power and discuss the possibility that a fraction of it can
be radiated in the X-ray range. We show that this reverse shock contribution
behaves in a way very similar to the observed X-ray afterglows if the following
two conditions are satisfied: (i) the Lorentz factor of the material which is
ejected during the late stages of source activity decreases to small values
Gamma < 10 and (ii) a large part of the shock dissipated energy is transferred
to a small fraction (zeta < 0.1) of the electron population. We also discuss
how our results may help to solve some puzzling problems raised by
multiwavelength early afterglow observations such as the presence of chromatic
breaks.
