Making use of 36 pb^-1 of proton–proton collision data at s√=7 TeV, the ATLAS Collaboration has performed a search for diphoton events with large missing transverse energy. Observing no excess of events above the Standard Model prediction, a 95% Confidence Level (CL) upper limit is set on the cross section for new physics of σ<0.38−0.65 pb in the context of a generalised model of gauge-mediated supersymmetry breaking (GGM) with a bino-like lightest neutralino, and of σ<0.18−0.23 pb in the context of a specific model with one universal extra dimension (UED). A 95% CL lower limit of 560 GeV, for bino masses above 50 GeV, is set on the GGM gluino mass, while a lower limit of 1/R>961 GeV is set on the UED compactification radius R. These limits provide the most stringent tests of these models to date.Instituto de Física La Plata