  Cross sections for the reactions gamma^(*) gamma^(*) --> hadrons and
gamma^(*) gamma^(*) --> 2 vector mesons are calculated as functions of energy
(sqrt(s) > 20 GeV) and photon virtualities. Good agreement with experiment is
obtained for the total hadronic cross section and, after allowing for a
valence-quark contribution from the hadronic part of the photon, with the
photon structure function at small x. The cross section for vector meson
production are shown to be experimentally accessible for moderate values of
Q^2. This is sufficient to probe the nature of the hard pomeron which has
recently been proposed.
