The moments of the single inclusive momentum distribution of hadrons in QCD jets are studied in the next-to-modified-leading-log approximation (NMLLA) including next-to-leading-order (NLO) corrections to the $\alpha_s$ strong coupling. The evolution equations are solved using a distorted Gaussian parametrisation, which successfully
reproduces the spectrum of charged hadrons of jets measured in electron positron annihilation experiments. The energy dependencies of the maximum peak, multiplicity, width, kurtosis and skewness of the jet hadron distribution are computed analytically. Comparisons of all the existing jet data measured in e+e- collisions in the range $\sqrt{s}=$~2--200~GeV$ to the NMLLA+NLO* predictions allow one to extract a value of the QCD mass scale $\Lambda_{QCD}$, and associated two-loop coupling constant at the Z0 resonance $\alpha_s{mZ}$~=~0.1195~$\pm$~0.0022, in excellent numerical agreement with the current world average obtained using other methods.
