  We discuss the two-gluon exchange contribution (formally three-loops) to
elastic photon-photon scattering in the high-energy approximation. The elastic
$\gamma\gamma \to \gamma \gamma$ amplitude is given in the impact-factor
representation for all helicity configurations and finite quark masses. We
discuss the importance of including the charm quark, which contribution, due to
interference, can enhance the cross section considerably. We investigate the
contribution to the $\gamma \gamma \to \gamma \gamma$ amplitude from the soft
region, by studying its dependence on nonperturbative gluon mass. Helicity-flip
contributions are shown to be much smaller than helicity-conserving ones. We
identify region(s) of phase space where the two-gluon exchange contribution
becomes important ingredient compared to box and nonperturbative VDM-Regge
mechanisms considered in the literature. Consequences for the $A A \to A A
\gamma \gamma$ reaction are discussed. Several differential distributions are
shown. A feasibility study to observe the effect of two-gluon exchange is
presented. We perform a similar analysis for the $p p \to p p \gamma \gamma$
reaction. Only by imposing severe cuts on $M_{\gamma \gamma}$ and a narrow
window on photon transverse momenta the two gluon contribution becomes
comparable to the box contribution but the corresponding cross section is
rather small.
