  We present the NNLO QCD virtual corrections for qurak-antiquark -> gluon
photon, quark-antiquark -> photon photon and the NNLO QED virtual corrections
for electron positron -> photon photon and all processes related by crossing
symmetry. We perform an explicit evaluation of the two-loop diagrams in
conventional dimensional regularisation, and our results are renormalised in
the MSbar scheme. The infrared pole structure of the amplitudes is in agreement
with the prediction of Catani's general formalism for the singularities of
two-loop amplitudes, while expressions for the finite remainder are given for
all processes in terms of logarithms and polylogarithms that are real in the
physical region.
