The process $\mathrm{e}^+\mathrm{e}^- \rightarrow n \gamma$ with $n\ge 2$ is studied at centre-of-mass energies ranging from $\sqrt{s}=192$ to $208$ GeV. The data sample corresponds to a total integrated luminosity of 427 pb$^{-1}$. The total and differential cross sections are found to be in agreement with the QED expectations. Using all the data collected with the L3 detector above the Z pole, limits on deviations from QED, excited electrons, contact interactions, extra space dimensions and excited spin-3/2 leptons are set.