  In the analysis of the total cross section for the gamma* gamma* -> hadrons
process, we include the four parton final states, which are part of the
O(alpha_s^2) corrections. The four-parton final states contain the diagrams
with gluon exchange in the crossed channel, which constitute the leading order
of the BFKL resummation. We show that the diagrams with gluon exchange in the
crossed channel play an important role in the large Y region, however their
contribution to the cross section must be evaluated exactly. In fact, the
high-energy limit, which constitutes the kinematic framework of the BFKL
resummation, is not sufficiently accurate at LEP2 energies. The inclusion of
the diagrams with gluon exchange in the crossed channel reduces the discrepancy
between the theory and the LEP2 data collected by the L3 Collaboration, but the
data still lie above the theory, even allowing for a large scale uncertainty in
the theory. Thus, in order to describe accurately the data for gamma* gamma* ->
hadrons in the large Y region, corrections of an order higher than O(alpha_s^2)
seem to be necessary.
