A study tested a multiple-resources model of human information processing wherein the two cerebral hemispheres are assumed to have separate, limited-capacity pools of undifferentiated resources. The subjects were five right-handed males who had demonstrated right visual field-left hemisphere (RVF-LH) superiority for processing a centrally presented verbal memory load and a nonsense syllable naming task in which the syllables were presented to either visual field. The subjects were paid according to their accuracy during both single and dual-task trials, with the payoff on the latter varied to induce more attention to the memory task, to the visual field naming task, or to both. Under moderate to heavy memory loads, the subjects who had shown large RVF single-task performance advantages for naming nonsense words showed larger performance decrements on RVF trials than on LVF trials in the dual-task situation; that is, both naming task and memory performance were superior when the naming task stimuli were presented to the left visual field. In addition, performance tradeoffs between tasks occurred on both types of visual field trials, thus providing evidence of overlap in demand. Overall, the experiment illustrated the prescribed methodology for testing models of limited-capacity processing, and the data supported the idea that there are at least two types of resource supplies, which are associated with processing in the left and right hemispheres. (RL)