Consideration was given to the model containing coupled subsystems (MCCS). With no connection between the subsystems, the MCCS falls down into independent subsystems, that is, systems of autonomous ordinary differential equations. MCCS with cycles in the subsystems were examined. For the autonomous MCCS, conditions were established for cycles and their stability, and a cycle stabilization by the control explicitly independent of time was proposed. For the periodic MCCS, generation of isolated periodic solutions was proved, and the problem of their stability and stabilization was solved.