Sighs prevent the collapse of alveoli in the lungs, initiate arousal under hypoxic conditions, and even express sadness and relief. Sighs are periodically superimposed on normal breaths, known as eupnea. Implicated in the generation of these rhythmic behaviors is the preBötzinger complex (preBötC)1. Yet how this small microcircuit can produce two rhythms with strikingly different periodicities remains unresolved. Our computational simulations predict that sighs are generated by the coincidence of two temporally distinct calcium oscillations and are in agreement with experimental evidence suggesting that astrocytes drive sigh behavior through slower, extrinsically driven calcium oscillations that link the eupnea and sigh rhythms. We found that purinergic signaling is necessary to generate spontaneous and hypoxia- induced sighs, and photo-activation of preBötC astrocytes is sufficient to elicit sigh activity. We conclude that sighs are an emergent property of the preBötC network generated by neuroglial interactions, where the distinct modulatory responses of neurons and glia allow for both rhythms to be independently regulated.