  Recently exact numerical results from the evolution equation for parton
multiplicities in QCD jets have been obtained. A comparison with various
approximate results is presented. A good description is obtained not only of
the jet multiplicities measured at LEP-1 but also of the hadron multiplicities
for $cms$ energies above 1.6 GeV in \epem annihilation. The solution suggests
that a final state hadron can be represented by a jet in the limit of small
(nonperturbative) $k_\perp$ cut-off $Q_0$. In this description using as
adjustable parameters only the QCD scale $\Lambda$ and the cut-off $Q_0$, the
coupling $\alpha_s$ can be seen to rise towards large values above unity at low
energies.
