This paper describes a measurement of the Michel parameters, eta, rho, xi,
xi delta, and the average v(tau) helicity, h(nu tau), in tau lepton decays
together with the first measurement of the tensor coupling in the weak char
ged current. The tau(+)tau(-) pairs were produced at the LEP e(+)e(-) colli
der at CERN from 1992 through 1995 in the DELPHI detector. Assuming lepton
universality in the decays of the tau the measured values of the parameters
were: eta = -0.005 +/- 0.036 +/- 0.037, rho = 0.775 +/- 0.023 +/- 0.020, x
i = 0.929 +/- 0.070 +/- 0.030, xi delta = 0.779 +/- 0.070 +/- 0.028, h(nu t
au) = -0.997 +/- 0.027 +/- 0.011. The strength ef the tensor coupling was m
easured to be kappa(tau)(W) = -0.029 +/- 0.036 +/- 0.018. The first error i
s statistical and the second error is systematic in all cases. The results
are consistent with the V - A structure of the weak charged current in deca
ys of the tau lepton.