The generation and shaping of the respiratory motor pattern are performed in the lower brainstem and involve neuronal interactions within the medulla and between the medulla and pons. A computational model of the ponto-medullary respiratory network has been developed by incorporating existing experimental data on the medullary neural circuits and possible interactions between the medulla and pons. The model reproduces a number of experimental findings concerning alterations of the respiratory pattern following various perturbations/stimulations applied to the pons and pulmonary afferents. The results of modeling support the concept that eupneic respiratory rhythm generation requires contribution of the pons whereas a gasping-like rhythm (and the rhythm observed in vitro) may be generated within the medulla and involve pacemaker-driven mechanisms localized within the medullary pre-Botzinger Complex. The model and experimental data described support the concept that during eupnea the respiration-related pontine structures control the medullary network mechanisms for respiratory phase transitions, suppress the intrinsic pacemaker-driven oscillations in the pre-BotC and provide inspiration-inhibitory and expiration-facilitatory reflexes which are independent of the pulmonary Hering-Breuer reflex but operate through the same medullary phase switching circuits.