Abstract: There are numerous binary systems in solar system. The research on binary systems is important for understanding the origin and evolution of asteroids. A two-triaxial-ellipsoid system is used to model the binary asteroids. Combining with Joshua's research in fourth-order mutual gravitational torque of two bodies, the stability of the binary system is proved by KTC theorem. Thus, the results verify a potential form of the doubly synchronous binary asteroids system where there is a roll angular velocity between the primary and moonlet.