Abstract: The local dynamics and periodic orbits in the vicinity of equilibrium points in binary asteroid systems are investigated. The dynamical model for synchronous binary asteroid system with one elongated asteroid and one small and regular asteroid is established. For the synchronous binary system, the influences of system parameters on location, stability, and variation trends of the equilibrium points are studied. The linear stability area for non-collinear equilibrium points is given. For the non-synchronous binary system, trajectories of equivalent equilibrium points are found. 1∶1 families of resonant orbits near the collinear equilibrium points of the synchronous binary asteroid system are obtained by the path searching correction method and the pseudo-arclength continuation method. This study can provide theoretical basis for the orbital design in binary asteroid explorations.