  In this paper, we continue to study pairwise ($k$-semi-)stratifiable
bitopological spaces. Some new characterizations of pairwise
$k$-semi-stratifiable bitopological spaces are provided. Relationships between
pairwise stratifiable and pairwise $k$-semi-stratifiable bitopological spaces
are further investigated, and an open question recently posed by Li and Lin in
\cite{LL} is completely solved. We also study the quasi-pseudo-metrizability of
a topological ordered space $(X, \tau, \preccurlyeq)$. It is shown that if $(X,
\tau, \preccurlyeq)$ is a ball transitive topological ordered $C$- and
$I$-space such that $\tau$ is metrizable, then its associated bitopological
space $(X,\tau^{\flat},\tau^{\natural})$ is quasi-pseudo-metrizable. This
result provides a partial affirmative answer to a problem in \cite{KM}.
