QCD evolution of hadron and jet multiplicity moments

We describe recent applications of the MLLA evolution equations to the calculation of mean multiplicities in quark and gluon jets and the higher moments of hadron and sub-jet multiplicity distributions in $e^{+}{e}^{-}$-annihilation as function of c.m.s. energy $Q$ and resolution parameter $y_{cut}$. The transition from jets to hadrons with increasing jet resolution is considered.