A model was tested in which it was assumed that the left and right cerebral hemispheres have access to independent supplies of resources, which they may use in most kinds of information processing situations. Eight male subjects were specifically selected for having demonstrated a strong right-hand superiority on several manual tasks, and a strong right visual field, left handed (RVF-LH) superiority for processing the stimuli used as a verbal memory load in a dual-task situation. Their performance was measured on the memory load task, on a target task in which pairs of stimuli were presented to either visual field and subjects performed physical or name identity judgments, and in a situation in which both tasks were combined. In this approach, right and left visual fields trials of the target task combined with the verbal memory load were treated as two different dual-task situations, comprising cases of complete vs. no overlap in demand for left hemisphere resources, respectively. The data support the idea that the resource supplies of the left and right hemispheres are independent, and have implications for both cerebral specialization and divided attention issues. (Author/JN)