We report on a search for compositeness in ee gamma events and a search for gauge-mediated supersymmetry in gamma gamma missing E(t) events. We also report on two signature-based searches for anomalous production of gamma gamma + X (where X = e, mu, gamma, missing E(t)) and gamma l + X (where X = missing E(t), l, gamma). The analyses are based on 0.9-1.2 fb-1 of data from p anti-p collisions at sqrt s = 1.96 TeV collected with the CDF and D0 detectors at the Fermilab Tevatron. No significant excess of data over the predicted background has been observed.