The nonlinear coupled dynamics of a rotating triangular tethered satellite formation near libration points is presented. Based on Hill' s approximation, a new dynamical formulation for a rotating triangular tethered system near libration points is developed. The formulation comprises a set of strong nonlinear coupled equations. Numerical simulations using the full nonlinear and time-varying motion equations are performed for the station-keeping stages. The dynamic characteristics of the triangular tethered formation are analyzed. The numerical results demonstrate that the rotating rate has a significant impact on the stability of the system, whereas the orbital amplitude has a moderate impact on the stability of the system. Tether length has little effect on the motion of the system's center of mass. It can be served as a basis to solve the problem of rotating triangular tethered systems in any arbitrary plane.