  Data from \epem annihilation into hadrons, collected by the \Jade experiment
at centre-of-mass energies between 14 GeV and 44 GeV, are used to study moments
of event shape distributions. Models with hadronisation parameters tuned to the
LEP 1 precision data provide an adequate description of the low energy data
studied here. The NLO QCD calculations, however, show systematic deficiencies
for some of the moments. The strong coupling measured from the moments which
are reasonably described by NLO QCD,
\asmz=0.1287\pm0.0007\stat\pm0.0011\expt\pm0.0022\had\pm0.0075\theo is
consistent with the world average.
