"Perturbative QCD and tau-decays"       

                                 Konstantin Chetyrkin




The current status of the higher order QCD corrections to the width of                                                        

the tau is discussed. We report on the result of the first complete                                                           

determination of the the strange quark mass to the order alpha_s^3.                                                           

We discuss the perspectives of the calculation of the not-yet-computed                                                        

contribution of order alpha_s^4 to the tau decay rate and its possible                                                        

influence on the extraction of the  value of the QCD coupling                                                                 

constant alpha_s from tau-decays.