Plug side connectors are prevented from moving relative to each other in the connecting/disconnecting direction, and one of the plug side connectors can be individually disconnected from the device side connector. The connector structure includes a longitudinal movement restricting protrusion on one of laterally facing side surfaces of the moveable member, which is resiliently deformably provided on the plug side housing, and a pair of stopper portions provided on another of the laterally facing side surfaces of the piece (48), and configured to restrict a movement of the longitudinal movement restricting protrusion of the laterally adjoining second housing (32) in the longitudinal direction by aligning with the longitudinal movement restricting protrusion (54) with respect to the longitudinal direction. When in an unlocked state, the longitudinal movement restricting protrusion (54) and the stopper portions (56, 58) are placed out of alignment with each other to release the restriction of the movement in the longitudinal direction.