During visual fixation, our eyes perform miniature eye movements—involuntarily and unconsciously. Using a random-walk analysis, we found a transition from persistent to anti-persistent correlations as a function of the time scale considered (Engbert and Kliegl, 2004 Psychological Science 15 431 - 436). This finding suggests functional dissociations of (i) the role of fixational eye movements on short and long time scales and (ii) between drift and microsaccades. Here we propose a mathematical model for the control of fixational eye movement based on the concept of time-delayed random-walks (Ohira and Milton, 1995 Physical Review E 52 3277 - 3280). Based on results obtained from numerical simulations we estimate time-delays within the brainstem circuitry underlying the control of fixational eye movements and microsaccades.