The results of investigation of a new phenomenon represented by the revolving of stiff rotor in elastic supports with four self-balanced pendulums are discussed in the article. The rotor is rotating with some operating velocity but the pendulums are moving with a frequency which equals one from two critical velocities of the rotor rotation connected with its linear or angular motion parameters. The procedure of mathematical models construction for system with eight degrees of freedom is offered. Dynamical interactions’ properties between partial systems with definite forms of a motion self-organization in a freely suspended pendulum group are discussed.