Automated monitoring of vigilance in attention intensive tasks such as air traffic control or sonar operation is highly desirable. As the opera(cid:173) tor monitors the instrument, the instrument would monitor the operator, insuring against lapses. We have taken a first step toward this goal by us(cid:173) ing feedforward neural networks trained with backpropagation to interpret event related potentials (ERPs) and electroencephalogram (EEG) associ(cid:173) ated with periods of high and low vigilance. The accuracy of our system on an ERP data set averaged over 28 minutes was 96%, better than the 83% accuracy obtained using linear discriminant analysis. Practical vigilance monitoring will require prediction over shorter time periods. We were able to average the ERP over as little as 2 minutes and still get 90% correct prediction of a vigilance measure. Additionally, we achieved similarly good performance using segments of EEG power spectrum as short as 56 sec.