Abstract An analysis based on 124 000 selected τ pairs recorded by the ALEPH detector at LEP provides the vector ( V) and axial-vector ( A) spectral functions of hadronic τ decays. The spectral functions of the dominant two-and four-pion vector τ decay modes are compared to published results of e + e − annihilation experiments applying isospin symmetry. A precise measurement of α s along with a determination of nonperturbative contributions at the τ mass scale is performed. The experimentally and theoretically most robust determination of α s ( M τ 2) is obtained from the ( V + A) fit that yields α s ( M τ 2) = 0.334 ± 0.022 giving α s ( M Z 2) = 0.1202 ± 0.0027 after the extrapolation to the mass of the Z boson. In addition, the approach of the Operator Product Expansion (OPE) is tested experimentally by studying the evolution of the τ hadronic widths to masses smaller than the τ mass. An analysis based on finite energy chiral sum rules provides a precise determination of the L 10 constant of the chiral lagrangian.