Consideration is given to the model containing coupled subsystems and obeying a system of ordinary differential equations (ODE) where the subsystems represent autonomous ODEs. The relations between subsystems is defined by the parameter ε; it is equal to zero, then the model decomposes into independent subsystems. MCCS may have one or more such parameters reflecting the hierarchical nature of its subsystems. In the general case, each subsystem has its own size and can be either linear or nonlinear, whereas its physical nature can be different. The N-planet problem where the subsystems lie at the same hierarchical level, multilink pendulum, coupled oscillators where the subsystems are connected serially, Sun-planet-satellites system, system of translatoryrotational celestial bodies representing the two-level hierarchical structures, robotic systems with possible cross-couplings, wind turbine representing an electromechanical system, model of DNA oscillations, coupled neurons, mechanotronic problems and others exemplify MCCS.