A study of W+W- events accompanied by hard photon radiation, E_gamma>2.5 GeV, produced in e+e- collisions at LEP is presented. Events consistent with being two on-shell W-bosons and an isolated photon are selected from 681 pb-1 of data recorded at 180 GeV < sqrt(s) < 209 GeV. From the sample of 187 selected W+W-gamma candidates with photon energies greater than 2.5 GeV, the W+W-gamma cross-section is determined at five values of sqrt(s). The results are consistent with the Standard Model expectation. Averaging over all energies, the ratio of the observed cross-section to the Standard Model expectation is
R(data/SM) = 0.99 +- 0.09 +- 0.04,
where the errors represent the statistical and systematic uncertainties respectively. These data provide constraints on the related O(alpha) systematic uncertainties on the measurement of the W-boson mass at LEP. Finally, the data are used to derive 95% confidence level upper limits on possible anomalous contributions to the W+W- gamma gamma and W+W-Z gamma vertices:
-0.020 GeV^-2 < & a_0/Lambda^2 & < 0.020 GeV^-2,
-0.053 GeV^-2 < & a_c/Lambda^2 & < 0.037 GeV^-2,
-0.16 GeV^-2 < & a_n/Lambda^2 & < 0.15 GeV^-2,
where Lambda represents the energy scale for new physics and a_0, a_c and a_n are dimensionless coupling constants.