  The orbital varieties are the irreducible components of the intersection
between a nilpotent orbit and a Borel subalgebra of the Lie algebra of a
reductive group. There is a geometric correspondence between orbital varieties
and irreducible components of Springer fibers. In type A, a construction due to
Richardson implies that every nilpotent orbit contains at least one smooth
orbital variety and every Springer fiber contains at least one smooth
component. In this paper, we show that this property is also true for the other
classical cases. Our proof uses the interpretation of Springer fibers as
varieties of isotropic flags and van Leeuwen's parametrization of their
components in terms of domino tableaux. In the exceptional cases, smooth
orbital varieties do not arise in every nilpotent orbit, as already noted by
Spaltenstein. We however give a (non-exhaustive) list of nilpotent orbits which
have this property. Our treatment of exceptional cases relies on an induction
procedure for orbital varieties, similar to the induction procedure for
nilpotent orbits.
