  The results of analysis of the one--loop spectrum of anomalous dimensions of
composite operators in the scalar $ \phi^{4} $ model are presented. We give the
rigorous constructive proof of the hypothesis on the hierarchical structure of
the spectrum of anomalous dimensions -- the naive sum of any two anomalous
dimensions generates a limit point in the spectrum. Arguments in favor of the
nonperturbative character of this result and the possible ways of a
generalization to other field theories are briefly discussed.
