1. Ventilation was measured in eleven healthy term infants during both quiet and active sleep, using the trunk plethysmograph, and instantaneous heart rate was derived from the electrocardiogram. Variations in individual respiratory and cardiac cycles were compared in each sleep state, and cross-correlations between ventilation and heart rate were used in the analysis of the data. 2. It was found that heart rate and respiratory rate were higher and more variable during active than during quiet sleep, with a small reduction in tidal volume. 3. Cross-correlations showed that respiratory sinus arrhythmia was present in both sleep states, but was more marked during quiet sleep. 4. Running cross-correlations using a 5 s window showed that phase relationships between ventilation and heart rate, were, on the whole, stable during quiet sleep, but markedly unstable during active sleep. 5. It is concluded that in the investigation of respiratory sinus arrhythmia in the new-born, it is important to take account of sleep state, the methods of measuring ventilation and heart rate, and to use analytical techniques suited to the specific purpose of the study. 6. Respiratory sinus arrhythmia is considered to be due to an interaction between systems controlling breathing and those controlling the cardiovascular system, and that this interaction is affected by sleep state.