The spectral functions of the vector current and the axial-vector current have been measured in hadronic ττ decays using the OPAL detector at LEP. Within the framework of the Operator Product Expansion a simultaneous determination of the strong coupling constant αsαs , 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 αs(m2τ)=0.348±0.009exp±0.019theoαs(mτ2)=0.348±0.009exp±0.019theo at the ττ -mass scale and αs(m2Z)=0.1219±0.0010exp±0.0017theoαs(mZ2)=0.1219±0.0010exp±0.0017theo at the Z0Z0 -mass scale. The values obtained for αs(m2Z)αs(mZ2) using Fixed Order Perturbation Theory or Renormalon Chain Resummation are 2.3% and 4.1% smaller, respectively. The ‘running’ of the strong coupling between s0≃1.3GeV2s0≃1.3GeV2 and s0=m2τs0=mτ2 has been tested from direct fits to the integrated differential hadronic decay rate Rτ(s0)Rτ(s0) . A test of the saturation of QCD sum rules at the ττ -mass scale has been performed.