Techniques are provided for treating periodic breathing, such as Cheyne-Stokes Respiration, using an implantable medical system. In one technique, diaphragmatic stimulation is delivered during a hyperpnea phase of periodic breathing via electrical stimulation of the phrenic nerves. Diaphragmatic stimulation is synchronized with intrinsic inspiration so as to increase the amplitude of diaphragmatic contraction during inspiration. This tends to decrease intrathoracic pressure leading to occlusion of the respiratory airway. Occlusion reduces actual ventilation during hyperpnea, thus reducing the cyclic blood chemistry imbalance that sustains periodic breathing so as to either mitigate periodic breathing or eliminate it completely. In another technique, respiration is instead inhibited during the hyperpnea phase of periodic breathing by blocking phrenic nerve signals to the extent necessary to reduce ventilation to terminate periodic breathing or at least mitigate its severity. Techniques are also described for controlling the type of therapy applied in response to periodic breathing.