Anomalous quartic couplings between the electroweak gauge bosons may contribute to the nu nu gamma gamma and qq gamma gamma final states produced in e+e- collisions. This analysis uses the LEP2 OPAL data sample at centre-of-mass energies up to 209 GeV. Event selections identify nu nu gamma gamma and qq gamma gamma events in which the two photons are reconstructed within the detector acceptance. The cross-section for the process e+e- --> qq gamma gamma is measured. Averaging over all energies, the ratio of the observed e+e- --> qq gamma gamma cross-section to the Standard Model expectation is
R(data}/SM) = 0.92 +- 0.07 +- 0.04,
where the errors represent the statistical and systematic uncertainties respectively. The nu nu gamma gamma and qq gamma gamma data are used to constrain possible anomalous WW gammagamma and ZZ gamma gamma couplings. Combining with previous OPAL results from the WW gamma final state, the 95% confidence level limits on the anomalous coupling parameters a0Z, acZ, a0W and acW are found to be:
-0.007 GeV^-2 < a0Z Lambda^2 < 0.023 GeV^-2,
-0.029 GeV^-2 < acZ Lambda^2 < 0.029 GeV^-2,
-0.020 GeV^-2 < a0W Lambda^2 < 0.020 GeV^-2,
-0.052 GeV^-2 < acW Lambda^2 < 0.037 GeV^-2,
where Lambda is the energy scale of the new physics. Limits found when allowing two or more parameters to vary are also presented.