  Integrable equations in ($1 + 1$) dimensions have their own higher order
integrable equations, like the KdV, mKdV and NLS hierarchies etc. In this paper
we consider whether integrable equations in ($2 + 1$) dimensions have also the
analogous hierarchies to those in ($1 + 1$) dimensions. Explicitly is discussed
the Bogoyavlenskii-Schiff(BS) equation. For the BS hierarchy, there appears an
ambiguity in the Painlev\'e test. Nevertheless, it may be concluded that the BS
hierarchy is integrable.
