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The electroencephalography (EEG) reflects the averaged electrical activity of large numbers of cortical neurons associated with different neural information processing of brain regions. Because EEG recording process is non-invasive, safe, and can be easily administered by clinicians, EEG signal analysis is considered to be a potential tool that may aid in the diagnosis of brain abnormalities including Alzheimer’s disease (AD). In this dissertation, we explore a variety of approaches to EEG signal modeling and analysis in order to characterize different brain states and conditions. We introduce novel versions of two existing approaches to EEG signal analysis: linear time-frequency approach suitable for non-stationary signals and stochastic dynamical approach suitable for evaluation of signal’s nonlinear properties and noise interaction. The former approach is mainly based on continuous wavelet transform (CWT) and discrete wavelet transform (DWT), while the latter approach involves reproduction of the EEG signal using a stochastic nonlinear oscillator model. In the wavelet transform approach, several wavelet basis functions are used to exclude biases resulting from the choice of mother wavelets. A variety of frequency and information entropic based features are then derived using each wavelet basis function. This approach is applied to EEG recordings from a pilot study of AD patients versus age-matched healthy normal subjects. Initially, statistically significant EEG features of AD patients are determined. Then, three different decision tree algorithms are applied to identify the most distinctive discriminant features. Finally, a novel index based on statistical significance, decision tree results, and rate of false classification is introduced to isolate the most reliable distinguishing EEG features of AD patients. In the second approach, a novel and unique approach is introduced to model the EEG signal as the output of a stochastic nonlinear dynamical system. Using a global optimization procedure, coupled Duffing van der Pol oscillator models subject to random excitation are selected to produce signals matching the frequency content, self-exciting limit cycle properties, and information entropic features of the EEG signal under different brain states and conditions. It is shown that there exists distinct models for healthy normal subjects and AD patients. It is further shown through these models that the EEG recordings from different brain states and conditions exhibit unique nonlinear properties such as relaxation oscillations and information entropic features. Thus, the models can be used to explore the nonlinear and noise-related features associated with brain disorders and injuries