  In a recent paper \cite{HuXi3}, we introduced a classes of derived
equivalences called almost $\nu$-stable derived equivalences. The most
important property is that an almost $\nu$-stable derived equivalence always
induces a stable equivalence of Morita type, which generalizes a well-known
result of Rickard: derived-equivalent self-injective algebras are stably
equivalent of Morita type. In this paper, we shall consider the compositions of
almost $\nu$-stable derived equivalences and their quasi-inverses, which is
called iterated almost $\nu$-stable derived equivalences. We give a sufficient
and necessary condition for a derived equivalence to be an iterated almost
$\nu$-stable derived equivalence, and give an explicit construction of the
stable equivalence functor induced by an iterated almost $\nu$-stable derived
equivalence. As a consequence, we get some new sufficient conditions for a
derived finite-dimensional algebras to induce a stable equivalence of Morita
type.
