Events with a final state consisting of two photons and large missing transverse energy have been observed in e+e- collisions at centre-of-mass energies in the range 192-209 GeV using the OPAL detector at LEP. Cross-section measurements are performed within the kinematic acceptance of the selection and compared with the expectations from the Standard Model process e+e- --> nu nu gamma gamma (gamma). No evidence for new physics contributions to this final state is observed. Upper limits on sigma(e+e- --> XX) * BR^2(X --> Y gamma) are derived for the case of stable and invisible Y. These limits apply to pair production of excited neutrinos (X = nu^*, Y = nu), to neutralino production (X = tilde(chi^0_2), Y = tilde(chi^0_1)) and to supersymmetric models in which X = tilde(chi^0_1) and Y = tilde(G) is a light gravitino.