New predictions for the behavior of multiplicity distributions in e+e-
collisions and their moments are obtained from the QCD equations for
generating functions of these distributions by taking nonlinear terms
into account more correctly than in commonly used approximations. The
role of quark degrees of freedom is shown to be insignificant. It is f
ound that the ratio of cumulant moments to factorial moments has a cha
racteristic minimum. The existence of this minimum is confirmed by the
experimental data and leads to the conclusion that the negative binom
ial distribution is inapplicable. The predictions of QCD are compared
with the most characteristic phenomenological distributions.