  Single- and multi-photon events with missing energy are selected in 619/pb of
data collected by the L3 detector at LEP at centre-of-mass energies between
189GeV and 209GeV. The cross sections of the process e^+e^- -> nu nu gamma
(gamma) 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_nu = 2.98 +/- 0.05 +/- 0.04. Selection results are also 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 1.5TeV
and 0.65TeV are set, at 95% confidence level, on the new scale of gravity for
the number of extra dimensions between 2 and 6.
