In this paper, we first give two optimal conditions for the sequences of intervals L 1 and L 2 such that each pair (P ;q i is bigraphic. One of them is optimal sufficient condition and the other one optimal necessary condition. We also present a characterization of (L 1 ; L 2 ) that is forcibly bigraphic on sequences of intervals. This is an extension of the well-known theorem on bigraphic sequences due to Gale and Ryser(see [4], [9]).