The recently described slow oscillations of amplitude of theta and alpha waves of the EEG (with a frequency below 0.08 Hz) in healthy subjects are attributed to the autonomic nervous system with control at the brain stem level. In the present pilot study, the slow brain rhythms were analyzed in a patient with Alzheimer’s disease and were compared to a healthy subject. Dynamic analysis of the EEG was performed using time-frequency mapping which gives simultaneous time and frequency representation of the brain signal. This method comprises a transform of the filtered EEG signal into its analytic form and application of the Wigner distribution modified by time and frequency smoothing. It has been shown that the envelope of both theta and alpha activities oscillates at 0.04 Hz and 0.07 Hz in the healthy subject and at 0.03 Hz and 0.06 Hz in a patient with Alzheimer’s disease. The amplitude of the slow oscillations of theta activity was substantially higher in the patient with Alzheimer’s disease as compared with the healthy subject. It is being proposed that the increase of slow brain rhythms in the patient with Alzheimer’s disease reflects an abnormal activity of the autonomic nervous system. However, the underlying pathophysiological mechanisms need to be further studied.