  The spectra of charged particles in the energy variable $\xi = \log 1/x$
(``the hump backed plateau'') are analyzed in terms of moments in order to
investigate the sensitivity to the running of $\alpha_s$ in particular towards
small scales, and to further test thereby the local parton hadron duality
picture. The modified leading log approximation (MLLA) of QCD provides a very
satisfying description of the $e^+e^-$ data in the full range of c.m. energies
from about 1 up to 91 GeV. The same calculation but with fixed coupling
$\alpha_s$ yields moments which are inconsistent with the data already close to
threshold. In particular the soft particles ($E\le 1$~GeV) reflect directly the
running of $\alpha_s$.
