Abstract: It is proved that a strongly
 connected oriented graph $D$ with $n\geq 4$ vertices and  at least ${n-1 \choose 2}+3$
 arcs has two distinct vertices $u^*, v^*$ such that both $D-u^*$ and $D-v^*$ are strongly connected. The examples
show that the above lower bound on the number of arcs is sharp.

Key words:  digraph,  , strongly connected subdigraph, critical vertex