  We have determined the strong coupling alpha-s from a comprehensive study of
energy-energy correlations (EEC) and their asymmetry (AEEC) in hadronic decays
of Z0 bosons collected by the SLD experiment at SLAC. The data were compared
with all four available predictions of QCD calculated up to O(alpha-s**2) in
perturbation theory, and also with a resummed calculation matched to all four
of these calculations. We find large discrepancies between alpha-s values
extracted from the different O(alpha-s**2) calculations. We also find a large
renormalization scale ambiguity in alpha-s determined from the EEC using the
O(alpha-s**2) calculations; this ambiguity is reduced in the case of the AEEC,
and is very small when the matched calculations are used. Averaging over all
calculations, and over the EEC and AEEC results, we obtain
alpha-s(MZ)=0.124+0.003-0.004(exp.) +-0.009(theory).
