Photonic events with large missing energy have been observed in e+e−e+e− collisions at centre-of-mass energies of 130, 136 and 183 GeV collected in 1997 using the OPAL detector at LEP. Results are presented for event topologies with a single photon and missing transverse energy or with an acoplanar photon pair. Cross-section measurements are performed within the kinematic acceptance of each selection. These results are compared with the expectations from the Standard Model process e+e−→νν¯¯¯e+e−→νν¯ + photon(s). No evidence is observed for new physics contributions to these final states. Using the data at s√s = 183 GeV, upper limits on σ(e+e−→XY)⋅BR(X→Yγ)σ(e+e−→XY)⋅BR(X→Yγ) and σ(e+e−→XX)⋅BR2(X→Yγ)σ(e+e−→XX)⋅BR2(X→Yγ) are derived for the case of stable and invisible Y. These limits apply to single and pair production of excited neutrinos (X=ν∗,Y=νX=ν∗,Y=ν), to neutralino production (X=χ~02,Y=χ~01X=χ~02,Y=χ~01) and to supersymmetric models in which X=χ~01X=χ~01 and Y=G~Y=G~ is a light gravitino.