  A semisimple element $s$ of a connected reductive group $G$ is said {\it
quasi-isolated} (respectively {\it isolated}) if $C_G(s)$ (respectively
$C_G^0(s)$) is not contained in a Levi subgroup of a proper parabolic subgroup
of $G$. We study properties of quasi-isolated semisimple elements and give a
classification in terms of the affine Dynkin diagram of $G$. Tables are
provided for adjoint simple groups.
