  Numerical Renormalization Group simulations have shown that the underscreened
spin-1 Kondo impurity model with power-law bath density of states (DOS)
$\rho(\w) \propto |\w|^r$ possesses various intermediate-coupling fixed points,
including a stable non-Fermi liquid phase. In this paper we discuss the
corresponding universal low-energy theories, obtain thermodynamic quantities
and critical exponents by renormalization group analysis together with suitable
$\epsilon$-expansions, and compare our results with numerical data. Whereas the
particle-hole symmetric critical point can be controlled at weak coupling using
a simple generalization of the spin-1/2 model, we show that the stable
non-Fermi liquid fixed point must be accessed near strong coupling via a
mapping onto an effective ferromagnetic $S_\mr{eff}=1/2$ model with singular
bath DOS with exponent $r_\mr{eff}=-r<0$. In addition, we consider the
particle-hole asymmetric critical fixed point, for which we propose a universal
field theory involving the crossing between doublet and triplet levels.
