Alzheimer's disease (AD) is the most common neurodegenerative disorder. Although a definite diagnosis is only possible by necropsy, a differential diagnosis with other types of dementia and with major depression should be attempted. The aim of this study was to analyse the electroencephalogram (EEG) background activity of AD patients to test the hypothesis that the regularity of the AD patients' EEG is higher than that of age-matched controls. We recorded the EEG from 19 scalp electrodes in 11 AD patients and 11 age-matched controls. Two different methods were used to estimate the regularity of the EEG background activity: spectral entropy (SpecEn) and sample entropy (SampEn). We did not find significant differences between AD patients and control subjects' EEGs with SpecEn. On the other hand, AD patients had significantly lower SampEn values than control subjects (p < 0.01) at electrodes P3, P4, O1 and O2. Our results show an increase of EEG regularity in AD patients. These findings suggest that nonlinear analysis of the EEG with SampEn could yield essential information and may contribute to increasing the insight into brain dysfunction in AD in ways which are not possible with more classical and conventional statistical methods.