  The spectrum of the anomalous dimensions of the composite operators (with
arbitrary number of fields $n$ and derivatives $l$) in the scalar $\phi^4$ -
theory in the first order of the $\epsilon$ -expansion is investigated. The
exact solution for the operators with number of fields $\leq 4$ is presented.
The behaviour of the anomalous dimensions in the large $l$ limit has been
analyzed. It is given the qualitative description of the %structure of the
spectrum for the arbitrary $n$.
