Based on the color dipole representation, we investigate consequences for t
he gamma*gamma*, gamma*gamma scattering of the finding by Fadin, Kuraev, an
d Lipatov that the incorporation of asymptotic freedom into the BFKL equati
on makes the QCD pomeron a series of isolated poles in the angular momentum
plane. The emerging color dipole BFKL-Regge factorization allows us to rel
ate in a model-independent way the contributions of each BFKL pole to the g
amma*gamma*, gamma*gamma scattering and the deep inelastic scattering on pr
otons. Numerical predictions based on our early work on the color dipole BF
KL phenomenology of the deep inelastic scattering on protons gives a good a
greement with the recent experimental data from OPAL and L3 experiments at
LEP200. We discuss the role of nonperturbative dynamics and predict a prono
unced effect of the Regge-factorization breaking due to large unfactorizabl
e nonperturbative corrections to the perturbative vacuum exchange. We comme
nt on the salient features of the BFKL-Regge expansion for the gamma*gamma*
, gamma*gamma scattering including the issue of the decoupling of subleadin
g BFKL poles and the soft plus rightmost hard BFKL pole dominance. (C) 2001
MAIK "Nauka/Interperiodica".