  Experimental data on the shape of hadronic momentum spectra are compared with
theoretical predictions in the context of calculations in the Modified Leading
Log Approximation (MLLA), under the assumption of Local Parton Hadron Duality
(LPHD). Considered are experimental measurements at $e^+e^-$-colliders of
$\xi_p^*$, the position of the maximum in the distribution of
$\xi_p=\log(1/x_p)$, where $x_p=p/p_{beam}$. The parameter $\xi_p^*$ is
determined for various hadrons at various centre of mass energies. It is
interesting to look at the dependence of $\xi^*_p$ on the hadron type. This is
used to study the influence of the hadron type on the cut-off scale $Q_0$ in
the parton shower development. The dependence of $\xi^*_p$ on the centre of
mass energy is seen to be described adequately by perturbation theory. The
approach is made quantitative by extracting a value of $\alpha_s(m_Z)$ from an
overall fit to the scaling behaviour of $\xi^*_p$.
