  We calculate the one-loop squared contributions to the
next-to-next-to-leading order ${\cal O}(\alpha^2\alpha_s^2)$ radiative QCD
corrections for the production of heavy quark pairs in the collisions of
unpolarized on--shell photons. In particular, we present analytical results for
the squared matrix elements that correspond to the product of the one--loop
amplitudes. All results of the perturbative calculation are given in the
dimensional regularization scheme. These results represent the Abelian part of
the corresponding gluon--induced next-to-next-to-leading order cross section
for heavy quark pair hadroproduction.
