We propose that extrapersonal space is represented in the brain by bimodal, visual-tactile neurons in: 1) inferior area 6 in the frontal lobe, 2) area 7b in the parietal lobe, and 3) the putamen.  In each of these areas, there are cells which respond both to tactile and visual stimuli.  In each area, the tactile receptive fields are arranged to form a somatotopic map.  The visual receptive fields are usually adjacent to the tactile ones and extend outward from the skin about 20 cm.  Thus each area contains a somatotopically organized map of the visual space that immediately surrounds the body.  These three areas are monosynaptically interconnected, and may form a distributed system for representing extrapersonal visual space.  For many neurons with tactile receptive fields on the arm or hand, when the arm was moved, the visual receptive field moved with it.  Thus, these neurons appear to code the location of visual stimuli in arm centered coordinates.  More generally, we suggest that the bimodal cells represent near, extrapersonal space in a body part centered fashion, rather than in an exclusively head centered or trunk centered fashion.