Results are presented from a study of the structure of high energy hadronic events recorded by the L3 detector at $\sqrt{s}\ge$ 192 GeV. The distributions of several event shape variables are compared to resummed $\cal{O}$$(\alpha_{\rm s}^{2})$ QCD calculations. We determine the strong coupling constant at three average centre-of-mass energies: 194.4, 200.2 and 206.2 GeV. These measurements, combined with previous L3 measurements at lower energies, demonstrate the running of $\alpha_{\rm s}$ as expected in QCD and yield $\alpha_{\rm s} (m_{\rm Z})$ = 0.1227 $\pm$ 0.0012 $\pm$ 0.0058, where the first uncertainty is experimental and the second is theoretical.