The contribution of interocular orientation differences to depth perception, at either the neuronal or the psychophysical level, is unclear. To understand the responses of binocular neurons to orientation disparity, we extended the energy model of Ohzawa et al. (1990) to incorporate binocular differences in receptive-field orientation. The responses of the model to grating stimuli with interocular orientation differences were examined, along with the responses to random dot stereograms (RDS) depicting slanted surfaces. The responses to combinations of stimulus orientations in the two eyes were left-right separable, which means there was no consistent response to the binocular orientation difference. All existing neuronal data concerning orientation disparity can be well described by this type of model (even a version with no disparity selectivity). The disparity sensitive model is nonetheless sensitive to changes in RDS slant, although it requires narrow orientation bandwidth to produce substantial modulation. The disparity-insensitive model shows no selectivity to slant in this stimulus. Several modifications to the model were attempted to improve its selectivity for orientation disparity and/or slant. A model built by summing several disparity-sensitive models showed left-right inseparable responses, responding maximally to a consistent orientation difference. Despite this property, the selectivity for slant in RDS stimuli was no better than the simple disparity-selective model. The range of models evaluated here demonstrate that interocular orientation differences are neither necessary nor sufficient for signaling slant. In contrast, within the framework of the energy model, positional disparity sensitivity appears to be both necessary and sufficient.