Continuous and simultaneous registration of electroencephalogram (EEG) and heart rate (HR) pattern in preterm infants can give information about the functioning of central nervous system and the integrity of the autonomic nervous system. The developmental and behavioural state determine the pattern of EEG activity. A discontinuous EEG activity also known as \'Trace alternant\' (TA) in preterm infants is accompanied by a low heart rate variability (HRV). It was found that electroencephalographic bursts of slow waves during TA are coupled with an acceleration of the HR. In this study, this synchronous behaviour of EEG bursts and HR is described for the first time in a group of preterm infants with a mean conceptional age (CA) of 36 weeks.