In an upright stance, individuals sway in unpredictable ways. Their eyes also move in unpredictable ways in fixation tasks. The objective of this study was to analyze visual functions, postural control, and cognitive involvement in stationary gaze. A total of 14 healthy young adults performed a fixation task and a free-viewing task (three trials per task, 45 s per trial). As expected, the results showed many ( = 32) significant positive Pearson correlation coefficients between the eye and center of pressure/body (head, neck, and lower back) movements in the fixation task. In the free-viewing task, the correlations were nonsignificant. Only 3 of the 32 significant correlations (9.4%) were significantly related to cognitive involvement (measured with a subjective questionnaire). These results indirectly strengthened the validity of the synergistic model of postural control.