The relationship between cognitive task demand and effect of bilateral advantage (BLA) was examined. In Experiment 1, the task demand based upon visual stimulus complexity was manipulated. One-digit and two-digit numbers were presented in the left, right or both visual fields tachistoscopically and subjects were requested to identify the numbers. The results showed no BLA, although a right visual field advantage was demonstrated. In Experiment 2, cognitive demand in terms of memory was manipulated. Subjects were asked to recall one-digit numbers that were presented successively once, three and five times in the left, right or the both visual fields. The results did not show any sign of BLA in the recall of numbers. In Experiment 3, a greater memory load task was given than that in Experiment 2, where two-digit numbers were presented successively (once, three and five times). Subjects were asked to recall the numbers. The results showed a significant BLA in the recall of numbers, i.e., the correct numbers in the correct temporal positions. These results strongly suggest that a benefit of redundant bilateral visual fields presentation is shown only in a highly cognitively demanding task, especially when it involves phonological memory loads.