Visual, auditory, and bimodal event-related potentials were recorded from 50 males, and lateral asymmetry indices were derived. Eleven psychometric tests of different cognitive attributes were also administered to them. This area of research has been labeled aptitude-treatment-interaction (ATI). The emphasis of ATI research is on identification of aptitude measures useful for selection of instructional treatments to maximize individual attainment of specified educational objectives. Principal factor analyses with varimax rotation were computed for asymmetry and cognitive measures. Some hemispheric asymmetries and cognitive attributes contributed to the same independent dimensions. Cerebral asymmetries accounted for more variance than cognitive characteristics. Converging support was provided that implicates the importance of lateral asymmetries for instructional research and development. Theoretical and practical propositions are presented which address whether cerebral lateralities can be considered as individual difference measures within an ATI conceptual framework. (Author/DWH)