  We study the diffractive production of photons in gamma-p and gamma-gamma
collisions. We specifically compute the rates for gamma*-p -> gamma-X and for
gamma*-gamma* -> gamma-gamma, where X denotes the proton dissociation. We focus
on the rates at large momentum transfers, -t >> Lambda^2, where we are most
confident in the use of QCD perturbation theory. However, our calculations do
allow us to study the -t -> 0 behaviour of the gamma*-gamma*-> gamma-gamma
process in the region where the incoming photons are sufficiently virtual.
