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The difference between the ratio of multiplicities and the ratio of theirderivatives on energy for gluon and quark jets is calculated up tonext-to-next-to leading order of perturbative QCD. Its non-zero value isuniquely defined by the running property of the QCD coupling constant. It isshown that this difference is rather small compared to values which can beobtained from experimental data. This disagreement can be ascribed either tostrong non-perturbative terms or to experimental problems with a scale choice,jets separation and inadequate assignement of soft particles to jets.Comment: 5 pages, LATEX, no Figs; submitted to JETP Let

Energy dependence of ratios of multiplicities and their slopes for gluon and quark jets