Sensitivity to binocular positional mismatch was evaluated in cat striate cortical neurones, for paired, dichoptically presented, moving sine-wave gratings whose interocular positional phase relationship was varied. Spatial frequency, orientation and velocity were optimized for each neurone. Binocular responses for each spatial phase were compared with monocular stimulation of either eye. Binocular responses ranged from facilitation, through complete or partial summation, to partial or binocular occlusion. Counter to previous reports, all functional classes of neurones (simple neurones; special, intermediate and standard complex neurones) were represented in phase-specific and phase-insensitive groups. Most simple neurones, together with a small minority of standard complex neurones, exhibited near-total phase-sensitive modulation, the most significant new finding being that a minority of simple neurones were relatively insensitive to binocular mismatch. The majority of complex neurones, of all types, showed shallower modulation depths (typically around 30%), distributed in a continuum, with no indication of bimodality. It is concluded that the property of positional sensitivity is not attributable solely to simple neurones; and that positional insensitivity is not seen only in complex neurones. At least some neurones of all functional categories evince either kind of behaviour. These results are interpreted as a two-stage mechanism for convergence and matching of inputs from the two eyes.