A general model is developed to account for all kinds of periodic breathing (PB) resulting from instability in respiratory control: in normals during sleep and on acute exposure to high altitude, in sleeping infants, and in patients with cardiovascular or neurologic lesions. It is found that in almost every case the ventilatory oscillation is mediated predominantly by the peripheral controller. System stability is decreased by hypoxia, hypercapnia, increased lung washout times, prolonged lung-chemoreceptor delays, and high controller sensitivity. Stability is enhanced by large lung CO2 and O2 storage volumes but little affected by body tissue stores. Using our own measurements of lung-ear delays, the model predicts that the mean cycle time of PB decreases from about 30 s at sea level to 20 s at 14,000 ft, in excellent agreement with data from other studies. Allometric scaling of the relevant parameters also shows close agreement between model predictions and data obtained on infants.