Were found the conditions for occurrence of dynamic auto-balancing for the case of a rotor mounted on two elastic-viscous supports, balanced by two or more passive auto-balancers of any type. A modernized energy method has been applied under assumption that the mass of auto-balancers’ loads is much smaller than the rotor mass. The method has been constructed for rotors on isotropic elastic-viscous supports, when such bodies are attached to the rotor, whose relative motion is hindered by elastic and viscous resistance forces. The method makes it possible to find stationary motions of the rotary system, assess their stability. At stationary motions the relative motions of the attached bodies stop, and the system rotates as a whole around the axis of rotation formed by the supports. The mechanical and mathematical model of the system has been described. We have found the generalized potential under stationary motions, as well as a dissipative function corresponding to the supports. For the generalized rotor coordinates the equations of stationary motions of the system have been derived. The reduced potential has been investigated for a conditional extremum under an assumption that the equations of stationary motions hold, which correspond to the generalized coordinates of the rotor. It has been established that dynamic balancing of the rotor is possible only for the case of a long rotor, two or more auto-balancers of any type, installed in different correction planes and only at the rotor rotation speeds exceeding resonance ones. It has been found that the resistance forces in the supports do not change the conditions for auto-balancing occurrence explicitly, but they can change these conditions implicitly ‒ by changing the region of existence of stationary motions. The result obtained coincides with the result that was derived from using a generalized empirical criterion for auto-balancing occurrence when damping in the supports is not taken into consideration. It has been shown that the modernized energy method (as well as the generalized empirical criterion for auto-balancing occurrence) makes it possible to find generalized conditions for auto-balancing occurrence, suitable for any type of auto-balancers. Therefore, both methods are applicable for building a general theory of passive auto-balancers, suitable for auto-balancers of any type.