Decrease of attention and an eventual microsleep of an artificial system operator is very dangerous and its early detection can prevent great losses. This chapter deals with a classification of states of vigilance based on analysis of an electroencefalographic activity of the brain. Preprocessing of data is done by the discrete Fourier transform. For the recognition radial basis functions (RBF), learning vector quantization (LVQ), multi-layer perceptron networks, k-nearest neighbor and a method based on Bayesian theory are used. Coefficients of bayes classifier are found using the maximum likelihood estimation. The experiments deal with analysis of human vigilance while their eyes are open. Then the reaction on visual stimuli is investigated. For this experiment 10 volunteers were repeatedly measured. The chapter shows that it is possible to classify vigilance in such conditions.