After a search on google, it seems to be a common problem on Asus UX series : On sceen side, the hinge is screwed in plastic frame, and because of fatigue, the plastic will break.
When it happens, the screen cover case is the piece to change ($80-$90), and the hinge may be replaced too ($15-$20 each). Some lubricant may be required to ease hinge movements.
Now : How to replace cover case ? In my case I have a touchscreen, and the piece and manipulation are not the same.