A real photon has a complicated nature, whereby it may remain unresolved or fluctuate into a vector meson or a perturbative q-qbar pair. In gamma-gamma events, this gives three by three combinations of the nature of the two incoming photons, and thus six distinct event classes. The properties of these classes are partly constrained by the choices already made in our related gamma-p model. It is therefore possible to predict the energy-dependence of the cross section for each of the six components separately. The total cross section gives support to the idea that a simple factorized ansatz with a pomeron and a reggeon term can be a good approximation. Event properties undergo a stepwise evolution from p-p to gamma-p to gamma-gamma events, with larger charged multiplicity, more transverse energy flow and a higher jet rate in the latter process.