The present invention relates to a flexible hinge device having a cooperative operating structure, comprising: a first plate and a second plate each having a top surface to which a flexible display screen having flexibility is attached; and a hinge unit configured to interconnects the first plate and the second plate and configured to be operated in a foldable manner so as to be bent or stretched, wherein the hinge unit comprises a plurality of segmental members connected to one another to allow the hinge unit to be bent or stretched, the first plate and the second plate are respectively coupled to the outermost segmental members positioned at both ends of the plurality of segmental members.