Many accidents are associated with a driver or machine operator's alertness level. Drowsiness often develops as a result of repetitive or monotonous tasks, uninterrupted by external stimuli. In order to enhance safety levels, it would be most desirable to monitor the individual's level of attention. In this work, changes in the power spectrum of the electroencephalographic signal (EEG) are associated with the subject's level of attention. This study reports on the initial research carried out in order to answer the following important questions: (i) Does a trend exist in the shape of the power spectrum, which will indicate the state of a subject's alertness state (drowsy, relaxed or alert)? (ii) What points on the cortex are most suitable to detect drowsiness and/or high alertness? (iii) What parameters in the power spectrum are most suitable to establish a workable alertness classification in human subjects? In this work, we answer these questions and combine power spectrum estimation and artificial neural network techniques to create a non-invasive and real - time system able to classify EEG into three levels of attention: High, Relaxed and Drowsiness. The classification is made every 10 seconds o more, a suitable time span for giving an alarm signal if the individual is with insufficient level of alertness. This time span is set by the user. The system was tested on twenty subjects. High and relaxed attention levels were measured in randomise hours of the day and drowsiness attention level was measured in the morning after one night of sleep deprivation.