It is shown that, as functions of their rank, cumulants of QCD multipl
icity distributions in small phase space bins possess quasi-oscillatin
g behavior similar to that found for them in the total rapidity range.
The first minimum moves to lower ranks for smaller bins. For the tota
l rapidity range, it moves to higher ranks with increasing energy. The
running property of the QCD coupling constant is in charge of these e
ffects, which can be verified in experiment.