The Michel parameters of the leptonic tau decays are measured using the OPAL detector at LEP. The Michel parameters 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 sqrt(s) = M(Z) corresponding to an integrated luminosity of 155 pb-1 during the years 1990 to 1995. If e-mu universality is assumed and inferring the tau polarization from neutral current data, the measured Michel parameters are extracted. 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.

32 pages, LaTeX, 9 eps figures included, submitted to the European Physical Journal C