Fusional limits of absolute retinal disparity between the two half-images of a large random-dot stereogram have been measured. The stereogram was viewed with disparity clamped at selected values (vergence loop opened), but without stabilization against conjugate eye movements, allowing the subject to look freely to different parts of the stereogram. Movements of both eyes were measured with a scleral coil technique. Limits for acquisition and retention of fusion were similar for the large stereogram. Total fusional ranges between 128 and 175 min arc were found in the different subjects. Limits for acquisition of fusion were smaller when fusion was preceded by prolonged stimulation with a large disparity (exceeding the fusional range) of the same direction (crossed or uncrossed). Thus, hysteresis between acquisition and retention was absent and the hysteresis present between loss of fusion and refusion was due to a reduction of the refusional limit. Probably this reduction is related to the recent history of binocular rivalry. Inspection of ocular vergence movements made during stimulation with constant or slowly changing disparity shows that neural remapping of retinal correspondence is rather unlikely.