  We prove that every digraph of circumference $l$ has DAG-width at most $l$
and this is best possible. As a consequence of our result we deduce that the
$k$-linkage problem is polynomially solvable for every fixed $k$ in the class
of digraphs with bounded circumference. This answers a question posed in
\cite{bangTCS562}. We also prove that the weak $k$-linkage problem (where we
ask for arc-disjoint paths) is polynomially solvable for every fixed $k$ in the
class of digraphs with circumference 2 as well as for digraphs with a bounded
number of disjoint cycles each of length at least 3. The case of bounded
circumference digraphs is open. Finally we prove that the minimum spanning
strong subdigraph problem is NP-hard on digraphs of DAG-width at most 5.
