The problem addressed in this work is sleepiness during driving, which often leads to accidents in the streets. Experiments with sleepy drivers took place and the EEG data were analysed in terms of non-linear methods. Sample entropy and phase synchronization variations were investigated within the signal sections corresponding to "driving events", i.e. driving mistakes or loss of control, as well as to periods of drowsiness and sleepiness, as compared to the periods of normal driving. Decreased sample entropy, indicating loss of complexity, and an increased phase synchronisation have been found in the preliminary study presented. The results are encouraging towards developing an alerting system for predicting and preventing driving accidents.