  Let $G=(V,E)$ be a twinless strongly connected graph. a vertex $v\in V$ is a
twinless articulation point if the subrgraph obtained from $G$ by removing the
vertex $v$ is not twinless strongly connected. An edge $e\in E$ is a twinless
bridge if the subgraph obtained from $G$ by deleting $e$ is not twiless
strongly connected graph. In this paper we study twinless articulation points
and twinless bridges. We also study the problem of finding a minimum
cardinality edge subset $E_{1} \subseteq E$ such that the subgraph $(V,E_{1})$
is twinless strongly connected. Moreover, we present an algorithm for computing
the $2$-vertex-twinless connected components of $G$.
