The total hadronic gamma*gamma* cross sections at high energy are calculate
d as a function of energy and photon virtuality in a model combining Reggeo
n exchange, the quark box diagram (a fixed pole in Regge language) and soft
and hard pomeron exchanges evaluated in the context of dipole-dipole scatt
ering. Goad agreement is obtained with the data for the real gamma gamma cr
oss section and for the real photon structure function F-2(gamma). However
the model prediction for the gamma*gamma* cross section is too small. This
is attributed to an incorrect extrapolation of the Q(2) dependence of the h
ard pomeron adopted here. Parametrising it independently shows that the har
d part of the cross section can be well represented by a simple Regge pole
with intercept similar to 1.3.