Equations of motion are derived for a satellite-stabilizer system. It is assumed that each stabilizer is coupled with the satellite through a one-degree-of-freedom viscoelastic suspension of the rotational or translational type. All equilibrium positions of the satellite-stabilizer system are determined. The two-stabilizer satellite is analyzed in detail. The conditions for stability near the equilibrium position are formulated for this case, and the rate-optimal parameters are determined.