  We generalize Monge property of real matrices for interval matrices. We
define two classes of interval matrices with Monge property - in a strong and
in a weak sense. We study fundamental properties of both classes. We show
several different characterizations of the strong Monge property. For weak
Monge property we give a polynomial characterization and several sufficient and
necessary conditions. For both classes we study closure properties. We further
propose a generalization of an algorithm by Deineko \& Filonenko which for a
given matrix returns row and column permutations such that the permuted matrix
is Monge if the permutations exist.
