A sample of 62249 tau-pair events is selected from data taken with the
ALEPH detector in 1991, 1992 and 1993. The measurement of the branchi
ng fractions for tau decays into electrons and muons is presented with
emphasis on the study of systematic effects from selection, particle
identification and decay classification. The results obtained are: B-e
=17.79+/-0.12(stat)+/-0.06(syst)(%) and B-mu=17.31+/-0.11(stat)+/-0.05
(syst)(%). Combined with the most recent ALEPH determination of the ta
u lifetime, these results provide a relative measurement of the lepton
ic couplings in the weak charged current for transverse W bosons: g(mu
)/g(e)=1.0002+/-0.0051 and g(tau)/g(mu)=0.9943+/-0.0065.