  In a number of systems, including certain semiconductors and unconventional
superconductors, the effective density of states varies near the Fermi energy
like $|E-E_F|^r$. The behavior of dilute magnetic impurities in such systems is
studied using a non-perturbative renormalization-group approach. Close to
particle-hole symmetry, the Kondo effect is suppressed for the cases of
greatest relevance ($r=1$ and $2$). Away from this symmetry, any quenching of
the impurity moment is accompanied by a low-temperature decrease in the
impurity resistivity, rather than the increase found in metals.
