The distributions of durations of fixations from infants and free-viewing adults are shown to be basically exponential for different stimulus conditions. It is found that fixation duration can be divided into two periods. One, the α-period, is a refractory period during which a saccade does not occur and fluctuates across fixations. The other, the β-period, is a random variable intrinsic to each fixation and constitutes a waiting-time for a saccade that occurs with constant probability per unit time. It is shown that mean duration decreases when stimulus size increases. These results suggest that fixations are terminated by saccades triggered by non-foveal stimulation.