  We compute the NNLO QCD corrections for the hadroproduction of a pair of
off-shell photons in the limit of a large number of quark flavors. We perform a
reduction of the two-loop amplitude to master integrals and calculate the
latter analytically as a Laurent series in the dimensional regulator using
modern integration methods. Real radiation corrections are evaluated
numerically with a direct subtraction of infrared limits which we cast in a
simple factorized form. The results presented here constitute a gauge invariant
part of the full NNLO corrections but are not necessarily dominant. We view
this calculation as a step towards a complete computation. Our partial
corrections to the total cross-section are about $1\%-3\%$ and vary with the
virtuality of the two off-shell photons.
