  We study one-loop corrections to the Chern-Simons coefficient $\kappa$ in
abelian self-dual Chern-Simons Higgs systems and their $N=2$ and $N=3$
supersymmetric generalizations in both symmetric and asymmetric phases.
One-loop corrections to the Chern-Simons coefficient of these systems turn out
to be integer multiples of $1/4\pi$ in both phases. Especially in the maximally
supersymmetric $N=3$ case, the correction in symmetric phase vanishes and that
in asymmetric phase is $\kappa/(2\pi |\kappa|)$. Our results suggest that
nonabelian self-dual systems might enjoy similar features. We also discuss
various issues arising from our results.
