We propose a minimalistic model of the anesthetized brain in order to study the generation of rhythms observed in electroencephalograms (EEGs) recorded from anesthetized humans. We propose that non-neuronal brain cells-astrocytes-play an important role in brain dynamics and that oscillation-based models may provide a simple way to study such dynamics. The model is capable of replicating the main features (i.e. slow and alpha oscillations) observed in EEGs. In addition, this model suggests that astrocytes are integral to the generation of slow EEG (∼0.7 Hz) rhythms. By including astrocytes in the model we take a first step towards investigating the interaction of the brain and cardiovasular system which are primarily connected via astrocytes. The model also illustrates that rich nonlinear dynamics can arise from basic oscillatory "building blocks" and therefore complex systems may be modelled in an uncomplicated way.