Photonic events with large missing energy have been observed in e+e−e+e− collisions at centre-of-mass energies of 130, 136, 161 and 172 GeV using the OPAL detector at LEP. Results are presented based on search topologies designed to select events with a single photon and missing transverse energy or events with a pair of acoplanar photons. In both search topologies, cross-section measurements are performed within the kinematic acceptance of the selection. These results are compared with the expectations from the Standard Model processes e+e−→νν¯¯¯γ(γ)e+e−→νν¯γ(γ) (single-photon) and e+e−→νν¯¯¯γγ(γ)e+e−→νν¯γγ(γ) (acoplanar-photons). No evidence is observed for new physics contributions to these final states. 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~20,Y=χ~10 ), and to supersymmetric models in which X=χ~01X=χ~10 and Y=G~Y=G~ is a light gravitino. For the latter scenario, the results of the acoplanar-photons search are used to provide mode l-dependent lower limits on the mass of the lightest neutralino.