An II x m matrix A is called bottleneck Monge matrix if max{ajj, a,,} < max{a,, ali} for all l<i<r<n, 1 < j < s < m. The matrix A is termed permuted bottleneck Monge matrix, if there exist row and column permutations such that the permuted matrix becomes a bottleneck Monge matrix. We first deal with the special case of Cl bottleneck Monge matrices. Next, we derive several fundamental properties...