The mechanical stabilization system for a support comprises a working rotor mounted on the support by means of bearings and fixed to a working member having at least one parameter associated with the rotation of the working member and which is variable as a function of time. A reaction rotor is concentric with the working rotor and is mounted on the working rotor by means of bearings and is fixed to a reaction inertia member. A first servo-controlled electric motor is interposed between the working rotor and the reaction rotor and serves to drive the working rotor and the reaction rotor in opposite directions of rotation. A low power second electric motor is interposed between the working rotor and the support and is servo-controlled in such a manner as to reposition the reaction rotor and correct for drift in the correcting motion of the reaction rotor, due in particular to friction in the bearings.