Wu and Grumbach introduced the concept of strongly biconnected directed
graphs. A directed graph G=(V,E) is called strongly biconnected if the
directed graph G is strongly connected and the underlying undirected graph of
G is biconnected. A strongly biconnected directed graph G=(V,E) is said to
be 2- edge strongly biconnected if it has at least three vertices and the
directed subgraph (V,Eβ{e}) is strongly
biconnected for all eβE. Let G=(V,E) be a 2-edge-strongly biconnected
directed graph. In this paper we study the problem of computing a minimum size
subset HβE such that the directed subgraph (V,H) is 2- edge
strongly biconnected