We analysed the electroencephalogram (EEG) from Alzheimer's disease (AD) patients with two non-linear methods: Approximate Entropy (ApEn) and Auto Mutual Information (AMI). ApEn quantifies regularity in data, while AMI detects linear and non-linear dependencies in time series. EEGs from 11 AD patients and 11 age-matched controls were analysed. ApEn was significantly lower in AD patients at electrodes O1, O2, P3 and P4 (p < 0.01). The EEG AMI decreased more slowly with time delays in patients than in controls, with significant differences at electrodes T5, T6, O1, O2, P3 and P4 (p < 0.01). The strong correlation between results from both methods shows that the AMI rate of decrease can be used to estimate the regularity in time series. Our work suggests that non-linear EEG analysis may contribute to increase the insight into brain dysfunction in AD, especially when different time scales are inspected, as is the case with AMI.