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In a previous article, we have shown that heart rate after birth depends strongly on age. This finding indicates significant changes in function or in postnatal maturation of heart rate control during the first half year of life. In the present work, we address the question as to whether the development of heart rate changes during sleep is associated with changes in its complexity and, thus, of the nonlinear components of the regulatory system. Heart rate parameters are modulated by sleep stages. Therefore we also determined how, and to what extent, sleep stages modulate the complexity of heart rate.