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.