The total hadronic gamma*gamma* cross sections at high energy are calculated as a function of energy and photon virtuality in a model combining Regge exchange, the quark box diagram (a fixed pole in Regge language) and soft and hard pomeron exchanges evaluated in the context of dipole-dipole scattering. Good agreement is obtained with the data for the real gamma-gamma cross section and for the real photon structure function. However the model prediction for the gamma* gamma* cross section is

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... cross section is too small. This is attributed to an incorrect extrapolation of the Q^2 dependence of the hard pomeron adopted here. Parametrising it independently shows that the hard part of the cross section can be well represented by a simple Regge pole with intercept ~ 1.3.