  We characterize locally semisimple subalgebras $\l$ of $\sl_\infty$,
$\so_\infty$, and $\sp_\infty$ which are Levi components of parabolic
subalgebras. Given $\l$, we characterize the parabolic subalgebras $\p$ such
that $\l$ is a Levi component of $\p$. When the set of such self-normalizing
parabolic subalgebras $\p$ is finite, we prove an estimate on its cardinality.
We consider various examples which highlight the differences from the case of
parabolic subalgebras of finite-dimensional simple Lie algebras.
