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In this talk we discuss the results obtained in the new approach that werecently introduced to consider and include both the perturbative andnonperturbative contributions to the evolution of the gluon and quark avaragemultiplicities. We report on our progresses in solving a longstanding puzzle ofQCD. The new formalism is motivated by recent important theoreticaldevelopments in timelike small-x resummation which are also discussed mostlyfrom an historical point of view. We have extended our global analysis to fitthe available data adding the strong coupling constant as a fit parameter. Inthis way our best fit gives $\alpha_s(M_z)=0.124\pm 0.005$ and for thecorresponding $\chi^2$ we have obtained a further improvement.

Timelike structure functions and hadron multiplicities