  It is well known that the Einstein equation on a Riemannian flag manifold
$(G/K,g)$ reduces to an algebraic system if $g$ is a $G$-invariant metric. In
this paper we obtain explicitly new invariant Einstein metrics on generalized
flag manifolds of $Sp(n)$ and $SO(2n)$; and we compute the Einstein system for
generalized flag manifolds of type $Sp(n)$. We also consider the isometric
problem for these Einstein metrics.
