  We explore the capability of the Tevatron and LHC as well as other future
hadron colliders to place limits on the possible existence of
flavor-independent $q \bar q \gamma\gamma$ contact interactions which can lead
to an excess of high $p_t$ diphoton events with large invariant masses.
Constraints on the corresponding $e^+e^-\gamma\gamma$ contact interaction
already exist from LEP. In the case of hadron colliders, strong constraints on
the scale associated with such interactions are achievable in all cases, e.g.,
of order 0.9(3) TeV at TeV33(LHC). [To appear in the Proceedings of the 1996
DPF/DPB Summer Study on New Directions for High Energy Physics-Snowmass96,
Snowmass, CO, 25 June-12 July, 1996.]
