Space electromagnetic formation is characterized mainly by advantages of no propellant consumption, no plume contaminations, continuous reversible and synchronous controllability, and static electromagnetic formation has a broad prospect of application in such fields as optical interferometry. The stability and control issues of dynamics equilibrium are the foundation for static electromagnetic formation. This research focused on the three equilibriums of two-spacecraft aligned with radial, along-track and normal direction, developed the 6-DOF coupled nonlinear dynamic models by the Kane method, and analyzed the open-loop stability, the coupled characteristics and the control requirements for each equilibrium respectively. Finally, an LQR feedback controller was designed and verified to stabilize the equilibriums.