  We explore self-dual Chern-Simons Higgs systems with the local $SU(3)$ and
global $U(1)$ symmetries where the matter field lies in the adjoint
representation. We show that there are three degenerate vacua of different
symmetries and study the unbroken symmetry and particle spectrum in each
vacuum. We classify the self-dual configurations into three types and study
their properties.
