The objective quantification of vigilance and sleepiness is more than ever an important focus in research. Impaired daytime vigilance due to insufficient sleep and low sleep quality has become an inevitable fact in industrialized countries. The reasons are manifold, the consequences may be fatal. Studies show that the loss of human life and also economic costs are substantial. The aim of this thesis is to objectively describe long-term daytime vigilance and sleepiness based on Electroencephalogram (EEG)-derived variables. We were able to provide significant empirical evidence for the circadian and homeostatic behavior of EEG-based variables. Our exploratory work is an important step towards objectively describing and predicting daytime vigilance and sleepiness. The positive results contribute to a better understanding of the representation of attentive processes in the EEG.