Continuous and repetitive performance of a task is likely to induce a drop in alertness levels of an individual. Changes in Electroencephalogram (EEG) have been proposed in literature as a marker of alertness during repeated performance of a cognitive task set. The present paper investigates the increase in fatigue levels and resultant drop in alertness of subjects during continuous performance of cognitive tasks by analyzing changes in energy of EEG frequency bands. The trends reflected in the EEG parameters correspond to a gradual increase in fatigue levels of subjects with increase in cognitive loading.