The Michel parameters of the leptonic ττ decays are measured using the OPAL detector at LEP. The parameters ρℓρℓ , ξℓξℓ , (ξδ)ℓ(ξδ)ℓ (with ℓ=e,μℓ=e,μ ) and ημημ are extracted from the energy spectra of the charged decay leptons and from their energy–energy correlations. A new method involving a global likelihood fit of Monte Carlo generated events with complete detector simulation and background treatment has been applied to the data recorded at center-of-mass energies close to s√=mZ0s=mZ0 corresponding to an integrated luminosity of 155 pb −1−1 . If e- μμ universality is assumed and inferring the ττ polarization from neutral current data, the measured Michel parameters are: where the value of ηη has been constrained using the published OPAL measurements of the leptonic branching ratios and the ττ lifetime. Limits on non-standard coupling constants and on the masses of new gauge bosons are obtained. The results are in agreement with the V–A prediction of the Standard Model.