  Anomalous quartic couplings between the electroweak gauge bosons may
contribute to the vv 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 vv 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 vv gamma gamma and qq gamma gamma data are used
to constrain possible anomalous W+W- gamma gamma and ZZ gamma gamma couplings.
Combining with previous OPAL results from the W+W- gamma final state, the 95%
confidence level limits on the anomalous coupling parameters aoz, acz, aow and
acw are found to be:
  -0.007 GeV^-2 < aoz/Lambda^2 < 0.023 GeV^-2 -0.029 GeV^-2 < acz/Lambda^2 <
0.029 GeV^-2 -0.020 GeV^-2 < aow/Lambda^2 < 0.020 GeV^-2 -0.052 GeV^-2 <
acw/Lambda^2 < 0.037 GeV^-2 where Lamdba is the energy scale of the new
physics. Limits found when allowing two or more parameters to vary are also
presented.
