We consider a periodic model containing coupled subsystems (MCCS), which, when the coupling between subsystems vanishes, decomposes into systems of autonomous ordinary differential equations. We assume that the subsystems admit different types of non-degenerate single-frequency oscillations. We solve the problems of the existence of oscillations in the MCCS, their stability, natural stabilization of MCCS oscillations by smooth time-periodic coupling controls. We also provide an example.