The chapter is organised in two parts: In the first part, the focus is on a combined power spectral and non-linear behavioural analysis of a neural mass model of the thalamocortical circuitry. The objective is to study the effectiveness of such “multi-modal” analytical techniques in model-based studies investigating the neural correlates of abnormal brain oscillations in Alzheimer’s disease (AD). The power spectral analysis presented here is a study of the “slowing” (decreasing dominant frequency of oscillation) within the alpha frequency band (8–13 Hz), a hallmark of electroencephalogram (EEG) dynamics in AD. Analysis of the non-linear dynamical behaviour focuses on the bifurcating property of the model. The results show that the alpha rhythmic content is maximal at close proximity to the bifurcation point—an observation made possible by the “multi-modal” approach adopted herein. Furthermore, a slowing in alpha rhythm is observed for increasing inhibitory connectivity—a consistent feature of our research into neuropathological oscillations associated with AD. In the second part, we have presented power spectral analysis on a model that implements multiple feed-forward and feed-back connectivities in the thalamo-cortico-thalamic circuitry, and is thus more advanced in terms of biological plausibility. This study looks at the effects of synaptic connectivity variation on the power spectra within the delta (1–3 Hz), theta (4–7 Hz), alpha (8–13 Hz) and beta (14–30 Hz) bands. An overall slowing of EEG with decreasing synaptic connectivity is observed, indicated by a decrease of power within alpha and beta bands and increase in power within the theta and delta bands. Thus, the model behaviour conforms to longitudinal studies in AD indicating an overall slowing of EEG.