  Let $D$ be a strong balanced digraph on $2a$ vertices. Adamus et al. have
proved that $D$ is hamiltonian if $d(u)+d(v)\ge 3a$ whenever $uv\notin A(D)$
and $vu\notin A(D)$. The lower bound $3a$ is tight. In this paper, we shall
show that the extremal digraph on this condition is two classes of digraphs
that can be clearly characterized. Moreover, we also show that if
$d(u)+d(v)\geq 3a-1$ whenever $uv\notin A(D)$ and $vu\notin A(D)$, then $D$ is
traceable. The lower bound $3a-1$ is tight.
