Generic scaling relation in the scalar $\phi^{4}$ model

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.