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The objective of the study was to test the heart rate variability (HRV) and the association between RR interval and the spontaneous respiration in a selected population of sick premature infants. Approximated Entropy (ApEn) and Regularity index were computed for RR series while four numerical indexes able to quantify association between signals were compared: (quadratic spectral coherence, linear correlation index, non linear association functions, and synchronization index). From a methodological point of view, both linear and non linear indexes were able to enhance the relationships between the signals. From a clinical point of view, lower relationships values were strongly associated with Sepsis Group while the Non Sepsis Group was characterized by a stronger relationship between RR series and the respiration. These results suggest that the exploration of RR and respiration relationships may help revealing systemic infection in premature newborns.