Driver sleepiness due to sleep deprivation is a causative factor in 1% to 3% of all motor vehicle crashes. In recent studies, the importance of developing driver fatigue countermeasure devices has been stressed, in order to help prevent driving accidents and errors. Although numerous physiological indicators are available to describe an individual's level of alertness, the EEG signal has been shown to be one of the most predictive and reliable, since it is a direct measure of brain activity. In the present study, multichannel EEG data that were collected from 20 sleep-deprived subjects during real environmental conditions of driving are presented for the first time. EEG data's annotation made by two independent Medical Doctors revealed an increase of slowing activity and an acute increase of the alpha waves 5-10 seconds before driving events. From the EEG data that were collected, the Relative Band Ratio (RBR) of the EEG frequency bands, the Shannon Entropy, and the Kullback-Leibler (KL) Entropy were estimated for each one second segment. The mean values of these measurements were estimated for 5 minutes periods. Analysis revealed a significant increase of alpha waves relevant band ratios (RBR), a decrease of gamma waves RBR, and a significant decrease of KL entropy when the first and the last 5-min periods were compared. A rapid decrease of both Shannon and K-L entropies was observed just before the driving events. Conclusively, EEG can assess effectively the brain activity alterations that occur a few seconds before sleeping/drowsiness events in driving, and its quantitative measurements can be used as potential sleepiness indicators for future development of driver fatigue countermeasure devices.