The research draws upon two separate areas of inquiry: that of lateralized electrocorical processing of cognitive material; and that of psychophysiological information processing studies related to foci of attentional demands. Eighteen subjects on each of three separate days were presented with tasks considered to be 'right hemispheric' or 'left hemispheric'. These tasks were paired in a 2 X 2 design with an attentional factor requiring attention to the environment or to internal processing. All subjects received all types of tasks. Bilateral EEG measures were taken from the frontal and parietal areas referenced to linked ears. Major frequency bands were determined by a Fast Fourier Transform (FFT) and appropriate ANOVAs performed. The results suggest that task factors (left vs right hemisphere tasks) and attentional demands (internal vs external) are differentially represented in terms of EEG functioning. In general the higher beta frequencies were more sensitive to the hemispheric tasks demands and the middle frequencies (alpha and low beta) more sensitive to the attentional demands especially in the parietal areas.