  The spectrum of critical exponents of the $N$--vector model in
$4-\eps$~dimensions is investigated to the second order in~$\eps$. A generic
class of one--loop degeneracies that has been reported in a previous work is
lifted in two--loop order. One-- and two--loop results lead to the conjecture
that the spectrum possesses a remarkable hierarchical structure: The naive sum
of any two anomalous dimensions generates a limit point in the spectrum, an
anomalous dimension plus a limit point generates a limit point of limit points
and so on. An infinite hierarchy of such limit points can be observed in the
spectrum.
