A steady opening and closing double-axis hinge comprises a first rotation member, a second rotation member and a connection member run through by the first rotation member and the second rotation member in a parallel manner. The first rotation member includes a first shaft and a first sector portion formed on the first shaft. The second rotation member includes a second shaft and a second sector portion formed on the second shaft. The connection member includes a movable detent plate which is located between the first and second shafts and movable between a first operation position and a second operation position. Through the movement of the movable detent plate, the first sector portion and second sector portion can be blocked alternately to control the first and second shafts to rotate in sequence, so as to simplify the shaft rotation switch mechanism and improve the durability.