  We formulate and analyse a saturation model for the total gamma gamma and
gamma* gamma* cross-sections and for the real photon structure function
F_2^gamma(x,Q^2). The model is based on a picture in which the gamma* gamma*
total cross-section for arbitrary photon virtualities is driven by the
interaction of colour dipoles, into which the virtual photons fluctuate. The
cross-section describing this interaction is assumed to satisfy the saturation
property with the saturation radius taken from the Golec-Biernat and Wusthoff
analysis of the gamma* p interaction at HERA. The model is supplemented by the
QPM and non-pomeron reggeon contributions. The model gives a very good
description of the data on the gamma gamma total cross-section, on the photon
structure function F_2^gamma(x,Q^2) at low x and on the gamma* gamma*
cross-section extracted from LEP double tagged events. Production of heavy
flavours in gamma gamma collisions is also studied. Predictions of the model
for the very high energy range which will be probed at future linear colliders
are given.
