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We study time series of RR intervals of subjects with normal sinus rhythm (NSR) during sleep and wake phases and we also analyze time series of subjects with congestive heart failure (CHF) in both phases with the method of Higuchi's fractal dimension. We have found the presence of oscillations in the plots we have used to evaluate the Higuchi's fractal dimension; these oscillations seem to be associated with the appearance of periodicities in the time series of CHF patients in the sleep phase. These periodicities do not appear in all the six hours of the sleep phase, so this regular behavior is not observed in all sleep stages. It could be possible that patients that always show these periodicities are in worst condition, and it is possible that the disease worsens when periodicities appear in the Higuchi's graph.