We present measurements of spectral moments extracted from the invaria
nt mass distributions of the final states of hadronic tau decay produc
ts recorded in the CLEO detector. From a fit of theoretical prediction
s to the measurements of spectral moments and the total hadronic decay
width of the tau, we determine the strong coupling constant and a set
of non-perturbative QCD parameters. The strong coupling constant is m
easured to be cr,(m,) = 0.306 +/- 0.024, which when extrapolated to th
e Z mass, yields alpha(s)(M(Z)) = 0.114 +/- 0.003.