Constraints on anomalous quartic gauge boson couplings from<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>ν</mml:mi><mml:mrow><mml:mrow><mml:mover><mml:mrow><mml:mi>ν</mml:mi></mml:mrow><mml:mrow><mml:mi>¯</mml:mi></mml:mrow></mml:mover></mml:mrow></mml:mrow><mml:mi>γ</mml:mi><mml:mi>γ</mml:mi></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>q</mml:mi><mml:mrow><mml:mrow><mml:mover><mml:mrow><mml:mi>q</mml:mi></mml:mrow><mml:mrow><mml:mi>¯</mml:mi></mml:mrow></mml:mover></mml:mrow></mml:mrow><mml:mi>γ</mml:mi><mml:mi>γ</mml:mi></mml:math>events at CERN LEP2

Anomalous quartic couplings between the electroweak gauge bosons may contribute to the $\ensuremath{\nu}\overline{\ensuremath{\nu}}\ensuremath{\gamma}\ensuremath{\gamma}$ and $q\overline{q}\ensuremath{\gamma}\ensuremath{\gamma}$ final states produced in ${e}^{+}{e}^{\ensuremath{-}}$ collisions. This analysis uses the LEP2 OPAL data sample at center-of-mass energies up to 209 GeV. Event selections identify $\ensuremath{\nu}\overline{\ensuremath{\nu}}\ensuremath{\gamma}\ensuremath{\gamma}$ and $q\overline{q}\ensuremath{\gamma}\ensuremath{\gamma}$ events in which the two photons are reconstructed within the detector acceptance. The cross section for the process ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}q\overline{q}\ensuremath{\gamma}\ensuremath{\gamma}$ is measured. Averaging over all energies, the ratio of the observed ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}q\overline{q}\ensuremath{\gamma}\ensuremath{\gamma}$ cross section to the standard model expectation is $\mathrm{R}(\mathrm{data}/\mathrm{SM})=0.92\ifmmode\pm\else\textpm\fi{}0.07\ifmmode\pm\else\textpm\fi{}0.04,$ where the errors represent the statistical and systematic uncertainties respectively. The $\ensuremath{\nu}\overline{\ensuremath{\nu}}\ensuremath{\gamma}\ensuremath{\gamma}$ and $q\overline{q}\ensuremath{\gamma}\ensuremath{\gamma}$ data are used to constrain possible anomalous ${W}^{+}{W}^{\ensuremath{-}}\ensuremath{\gamma}\ensuremath{\gamma}$ and $\mathrm{ZZ}\ensuremath{\gamma}\ensuremath{\gamma}$ couplings. Combining with previous OPAL results from the ${W}^{+}{W}^{\ensuremath{-}}\ensuremath{\gamma}$ final state, the 95% confidence level limits on the anomalous coupling parameters ${a}_{0}^{\mathrm{Z}},$ ${a}_{\mathrm{c}}^{\mathrm{Z}},$ ${a}_{0}^{\mathrm{W}}$ and ${a}_{\mathrm{c}}^{\mathrm{W}}$ are found to be $\ensuremath{-}0.007 {\mathrm{GeV}}^{\ensuremath{-}2}&lt;{a}_{0}^{\mathrm{Z}}/{\ensuremath{\Lambda}}^{2}&lt;0.023 {\mathrm{GeV}}^{\ensuremath{-}2},$ $\ensuremath{-}0.029 {\mathrm{GeV}}^{\ensuremath{-}2}&lt;{a}_{\mathrm{c}}^{\mathrm{Z}}/{\ensuremath{\Lambda}}^{2}&lt;0.029 {\mathrm{GeV}}^{\ensuremath{-}2},$ $\ensuremath{-}0.020 {\mathrm{GeV}}^{\ensuremath{-}2}&lt;{a}_{0}^{\mathrm{W}}/{\ensuremath{\Lambda}}^{2}&lt;0.020 {\mathrm{GeV}}^{\ensuremath{-}2},$ $\ensuremath{-}0.052 {\mathrm{GeV}}^{\ensuremath{-}2}&lt;{a}_{\mathrm{c}}^{\mathrm{W}}/{\ensuremath{\Lambda}}^{2}&lt;0.037 {\mathrm{GeV}}^{\ensuremath{-}2},$ where $\ensuremath{\Lambda}$ is the energy scale of the new physics. Limits found when allowing two or more parameters to vary are also presented.