  A complete numerical solution of the evolution equation for parton
multiplicities in quark and gluon jets with initial conditions at threshold is
presented. Data on both hadron and jet multiplicities in e+e- annihilation are
well described with a common normalization, giving further support to the
picture of Local Parton Hadron Duality. Predictions for LEP-II energies are
presented. Furthermore we study the sensitivity to the cutoff parameter Q_0 and
the scale of alpha_s.
