The model containing coupled subsystems (MCCS), which decouples into independent subsystems as the coupling vanishes, is considered. The subsystems of the MCCS are described by autonomous systems of ordinary differential equations. Each subsystem is supposed to admit a single parameter family of periodic motions. The general characteristics of the MCCS are presented. Some problems concerning the MCCS are stated, i.e. the problems of oscillations existence, bifurcations, stability, stabilization, and resonance. The classification of MCCS is proposed, the currently investigated classes of MCCS are announced. One class of MCCS is studied in detail, the corresponding results are presented.