  The strong coupling constant alpha_S is determined using recently re-analysed
e+e- annihilation data collected by the JADE experiment at sqrt{s}= 14 to 44
GeV. The measurements are based on O(alpha_S**2)+NLLA predictions for various
event shape observables. The calculations are found to describe reliably data
at the lowest energies of the e+e- continuum where non-perturbative
contributions become important. The results for alpha_S are in good agreement
with the QCD expectation for the running of the strong coupling constant. This
is the first determination of alpha_S at sqrt{s}= 14 and 22 GeV based on
resummed QCD predictions.
