To identify neuronal mechanisms underlying stereopsis, we characterized interactions between inputs from the two eyes in disparity-selective neurons in macaque V1. All disparity-selective cells showed suppressive interactions between the right and left eyes, and some showed facilitatory interactions. Disparity selectivity was narrower than the receptive-field width and was constant across the receptive field. Such position-invariant disparity selectivity is also found in anesthetized cat V1. Complex cells have been suggested to inherit their disparity selectivity from simple cells with receptive fields mismatched between the two eyes. However, we found no such antecedent disparity-tuned simple cells. We did find disparity-selective cells with some simple-cell characteristics, but surprisingly, they also showed position-invariant disparity selectivity rather than simple linear binocular interactions.