  The perturbative QCD approach to multiparticle production assuming Local
Parton Hadron Duality (LPHD) and some recent results are discussed. Finite
asymptotic scaling limits are obtained for various observables, after an
appropriate rescaling, in the Double Logarithmic Approximation (DLA).
Non-asymptotic corrections are also known in some cases. The DLA applies also
to very soft particle production where energy conservation constraints can be
neglected. In this region the particle density follows rather well a scaling
behaviour over the full energy range explored so far in $e^+e^-$ annihilation.
