  Though the predictions of the Standard Model (SM) are in excellent agreement
with experiments there are still several theoretical problems, such as
fine-tuning and the hierarchy problem. These problems are associated with the
Higgs sector of the SM, where it is widely believed that some {\it ``new
physics"} will take over at the TeV scale. One beyond the SM theory which
resolves these problems is the Little Higgs (LH) model. In this work we shall
investigate the effects of the LH model on $\gggg$ scattering; where the
process $\gggg$ at high energies occurs in the SM through diagrams involving
$W$, charged quark and lepton loops (and is, therefore, particularly sensitive
to any new physics
