Fender and Julesz [J. Opt. Soc. Am. 57, 819 (1967)] found that fused retinally stabilized binocular line targets could be misaligned on the two retinas in the temporalward direction by at least 30 min of arc without loss of fusion and stereopsis and that random-dot stereograms could be misaligned 2 deg before fusion was lost. To test these results in normal vision, we recorded eye motions of four observers while they viewed a random-dot stereogram that subtended about 10 deg. The observers misaligned overlaid vectograph stereo images by moving them apart in a temporalward direction until fusion was lost. They then returned the vectographs to the overlaid position. Throughout this cycle the observers reported at frequent intervals if they could perceive strong or weak depth, loss of depth, or loss of fusion. For some observers the image separation could be increased to 5 deg beyond parallel before fusion was lost. The visual axes diverged to follow the image centers and varied from overconverged to overdiverged with respect to the image centers while the observers still reported depth and fusion. We call the difference between the image separation and eye vergence the vergence error. If a vergence error persisted for at least 10 sec without loss of the percepts of fusion and depth, we postulate that neutral remapping occurred that compensated for the retinal misalignment. We found that the average maximum neural remapping was 3.0 deg.(ABSTRACT TRUNCATED AT 250 WORDS)