A spatio-temporal wavelet-chaos methodology is presented for analysis of EEGs and their delta, theta, alpha, and beta sub-bands for discovering potential markers of abnormality in Alzheimer's disease (AD). The non-linear dynamics of the EEG and EEG sub-bands are quantified in the form of the correlation dimension (CD), representing system complexity, and the largest Lyapunov exponent (LLE), representing system chaoticity. The methodology is applied to two groups of EEGs: healthy subjects and AD patients. The eyes open and eyes closed conditions are investigated to evaluate the effect of visual input and attention. EEGs from different loci in the brain are investigated to discover areas of the brain responsible for or affected by changes in CD and LLE. It is found that the wavelet-chaos methodology and the sub-band analysis developed in this research accurately characterizes the non-linear dynamics of non-stationary EEG-like signals with respect to the EEG complexity and chaoticity. It is concluded that changes in the brain dynamics are not spread out equally across the spectrum of the EEG and over the entire brain, but are localized to certain frequency bands and electrode loci. New potential markers of abnormality were discovered in this research for both eyes open and closed conditions.