The goal of this study was to investigate the EEG signs of early stage Alzheimer's disease (AD) by conventional analyses and by methods quantifying linear and nonlinear EEG-complexity. The EEG was recorded in 12 mild AD patients and in an age-matched healthy control group (24 subjects) in both eyes open and eyes closed conditions. Frequency spectra, Omega-complexity and Synchronization likelihood were calculated on the data. In the patients a significant decrease of the relative alpha and increase of the theta power were found. Remarkably increased Omega-complexity and lower Synchronization likelihood were observed in AD in the 0.5-25 Hz frequency ranges. It is concluded that both spectral- and EEG-complexity changes can be found already in the early stage of AD in a wide frequency range. Application of conventional EEG analysis methods in combination with quantification of EEG-complexity may improve the chances of early diagnosis of AD.