  We obtain a simple analytic expression for the high energy $\gamma^*
\gamma^*$ scattering cross section at the next-to-leading order in the
logarithms-of-energy power counting. To this end we employ the eigenfunctions
of the NLO BFKL equation constructed in our previous paper. We also construct
the eigenfunctions of the NNLO BFKL kernel and obtain a general form of the
solution for the NNLO BFKL equation, which confirms the ansatz proposed in our
previous paper.
