A bipartite -digraph is an orientation of a bipartite multigraph that is without loops and contains at most edges between any pair of vertices from distinct parts. In this paper, we obtain necessary and sufficient conditions for a pair of sequences of non-negative integers in non-decreasing order to be a pair of sequences of numbers, called marks (or -scores), attached to the vertices of a bipartite -digraph. These characterizations provide algorithms for constructing the corresponding bipartite multi-digraph.