  The spectral functions of the vector current and the axial-vector current
have been measured in hadronic tau decays using the OPAL detector at LEP.
Within the framework of the Operator Product Expansion a simultaneous
determination of the strong coupling constant alpha_s, the non-perturbative
operators of dimension 6 and 8 and of the gluon condensate has been performed.
Different perturbative descriptions have been compared to the data. The Contour
Improved Fixed Order Perturbation Theory gives alpha_s(mtau**2) = 0.348 +-
0.009 +- 0.019 at the tau-mass scale and alpha_s(mz**2) = 0.1219 +- 0.0010 +-
0.0017 at the Z-mass scale. The values obtained for alpha_s(mz**2) using Fixed
Order Perturbation Theory or Renormalon Chain Resummation are 2.3% and 4.1%
smaller, respectively. The running of the strong coupling between s_0 ~1.3
GeV**2 and s_0 = mtau**2 has been tested from direct fits to the integrated
differential hadronic decay rate R_tau. A test of the saturation of QCD sum
rules at the tau-mass scale has been performed.
