Abstract: A simple digraph D (without loops and multiple arcs) is said to be super-connected if every minimum vertex-cut is the out-neighbor set or in-neighbor set of a vertex. A super-connected digraph D is said to be bi-super-connected if there exists a minimum vertex-cut is both the out-neighbor set of a vertex and the in-neighbor set of a vertex. In this paper, we will give the necessary and sufficient conditions of line digraph is bi-super-connected, furthermore, we study the big super-connectivity of Cartesian product and lexicographic product of two digraphs.

Key words: combinatorial problems, super-connected;bi-super-connected, line digraphs, Cartesianproduct