  We consider a general model, describing a quantum impurity with degenerate
energy levels, interacting with a gas of itinerant electrons, derive general
scaling equation for the model, and analyse the connection between its
particular forms and the symmetry of interaction. On the basis of this analysis
we write down scaling equations for the Hamiltonians which are the direct
products of $su(3)$ Lie algebras and have either $SU(2)\times U(1)$ or $SU(2)$
symmetry. We also put into a new context anisotropic Coqblin -- Schrieffer
models proposed by us earlier.
