This paper is dedicated to the attitude control law synthesis for GRACE-like missions. Namely, two satellites move along the same orbit at a distance of several hundred kilometers and "look" at each other. This angular motion resembles the stabilization at unstable equilibrium position in the Orbital Frame. The reaction wheels cannot be used because they greatly affect the accelerometers measurements. Hence, only magnetorquers and thrusters may be utilized for the attitude control. Two different approaches are considered: linear quadratic regulator and Lyapunov-based controller. Control coefficients of the latter are obtained using the Floquet theory. Numerical simulation including atmospheric drag, solar radiation pressure and state vector measurements errors is carried out to validate suggested control techniques. The developed attitude determination and control system algorithms are tested for GRACE and GRACE-FO mission scenarios with relevant requirements and parameters.