Discriminant analysis and EEG source localization methods were employed to compare groups of normal subjects during different cognitive conditions using 43-channel EEG recordings in the alpha (8-13 Hz) frequency band. Recordings were obtained from 69 dextral females during 2 passive conditions, Eyes-Open and Eyes-Closed, and 2 active conditions, Word-Finding and Dot-Localization. The cross-spectral matrix between all of the electrode sites was used to characterize the EEGs obtained during each condition. The subjects were partitioned into training and test sets and quadratic discriminant functions were constructed from the training sets to classify the EEGs. The discriminant functions successfully classified both the training and test sets at rates approaching 80%. The classification was repeated using only the diagonal (power spectral) elements of the cross-spectral matrices in the discriminant functions and this approach was successful in discriminating between the EEGs from the passive cognitive conditions but failed to discriminate between the EEGs from the active conditions. Source localization using a modified MUSIC algorithm indicated that the centers of brain electrical activity that distinguished the Eyes-Closed condition from the Eyes-Open condition were located in the medial occipital and right frontal regions. Centers of electrical activity that distinguished the Word-Finding condition from the Dot-Localization condition were located in the right medial posterior and left temporal regions. Validation of the locations of the centers of activity was accomplished by repeating the classification procedures using the spatial patterns generated on the scalp by dipole current sources placed at these locations.