Consideration was given to the model containing coupled subsystems (MCCS). In the
absence of coupling, MCCS falls down into independent subsystems represented by autonomous
ordinary differential equations (ODE). In the structure of the entire system its subsystems make
up hierarchical levels. The autonomous MCCS was studied. The “cycle or family of periodic
motions” alternative was shown to be always realized by an individual system in a nondegenerate
situation. For the main mode of oscillations, a scenario was given for bifurcation of the family
of all families of periodic solutions arising with generation of the MCCS cycles. Consideration
was given to stability of cycles, and the problem of their stabilization was solved.