Single- and multi-photon events with missing energy are selected in 619 pb-1 of data collected by the L3 detector at LEP at centre-of-mass energies between 189 and 209 GeV. The cross sections of the process e +e-→νν̄γ(γ) are found to be in agreement with the Standard Model expectations, and the number of light neutrino species is determined, including lower energy data, to be N ν=2.98±0.05±0.04. Selection results are given in the form of tables which can be used to test future models involving single- and multi-photon signatures at LEP. These final states are also predicted by models with large extra dimensions and by several supersymmetric models. No evidence for such models is found. Among others, lower limits between 1.5 and 0.65 TeV are set, at 95% confidence level, on the new scale of gravity for the number of extra dimensions between 2 and 6. © 2004 Published by Elsevier B.V.