Unlike older children, young infants are prone to develop unstable respiratory patterns, suggesting important differences in their control of breathing. We examined the irregular breathing pattern in infants by measuring the time interval between breaths ("interbreath interval"; IBI) assessed from abdominal movement during 2 h of sleep in 25 preterm infants at a postconceptional age of 40.5 ± 5.2 (SD) wk and in 14 term healthy infants at a postnatal age of 8.2 ± 4 wk. In 10 infants we performed longitudinal measurements on two occasions. We developed a threshold algorithm for the detection of a breath so that an IBI included an apneic period and potentially some periods of insufficient tidal breathing excursions (hypopneas). The probability density distribution (P) of IBIs follows a power law, P(IBI)~IBI, with the exponent  providing a statistical measurement of the relative risk of insufficient breathing. With maturation,  increased from 2.62 ± 0.4 at 41.2 ± 3.6 wk to 3.22 ± 0.4 at 47.3 ± 6.4 wk postconceptional age, indicating a decrease in long hypopneas (for paired data P = 0.002). The statistical properties of IBI were well reproduced in a model of the respiratory oscillator on the basis of two hypotheses: 1) tonic neural inputs to the respiratory oscillator are noisy; and 2) the noise explores a critical region where IBI diverges with decreasing tonic inputs. Accordingly, maturation of infant respiratory control can be explained by the tonic inputs moving away from this critical region. We conclude that breathing irregularities in infants can be characterized by , which provides a link between clinically accessible data and the neurophysiology of the respiratory oscillator.