Latent disturbances in the control of respiration and heart rate (HR) may be important factors in the pathogenesis of life-threatening events during infancy. A method of determining the control of the autonomic nervous system functions involves the analysis of time-dependent ultradian changes of its parameters. The breathing signal and HR variability contain rhythmic components that are generated within the cardiorespiratory network of the brain stem, through reflexes, and by feedback mechanisms. The analysis of these components may provide insights into the functioning of the cardiorespiratory control system. The prominence and precision of the rhythms are correlated with states of vigilance and underlie distinct development during the first months of life. The results of studies on infants at risk (for example, for sudden infant death), with the help of statistical and spectral analysis of time series to obtain new indices, have proved to be inconsistent in their prognostic value of thus studied parameters. Recently, the importance of qualitative and quantitative assessment of the dynamic and complex behavior of time series, based on nonlinear characteristics of the control system, has been emphasized. To what extent, however, the analysis of the dynamic behavior can be utilized for clinical purposes, such as judging the prognosis of deficiencies in control, requires further study regarding physiological baselines and the possible changes resulting from pathological states.