Ninety-one right brain-damaged patients with left neglect and 43 right brain-damaged patients without neglect were asked to extend horizontal segments, either left- or rightward, starting from their right or left endpoints, respectively. Earlier experiments based on similar tasks had shown, in left neglect patients, a tendency to overextend segments toward the left side. This seemingly paradoxical phenomenon was held to undermine current explanations of unilateral neglect. The results of the present extensive research demonstrate that contralesional overextension is also evident in (...) most right brain-damaged patients without contralesional neglect. Furthermore, they show that in a minority of left neglect patients, the opposite behavior, i.e., right overextension can be found. The paper also reports the results of correlational analyses comprising the parameters of line-extension, line-bisection, and cancellation tasks, as well as the parameters relative to the Milner Landmark Task, by which a distinction is drawn between perceptual and response biases in unilateral neglect. A working hypothesis is then advanced about the brain dysfunction underlying neglect and an attempt is made at finding an explanation of neglect and the links between the mechanisms of space representation and consciousness through the study of the changes induced by unilateral brain lesions in the characteristics of space-coding neurons. Abbreviations: C, control group;GN+91,full group of neglect patients;GN+27,group of neglect patients with relative left overextension;GN+14,group of neglect patients with relative right overextension;GN-43,full group of non-neglect patients;GN-9,group of non-neglect patients with relative left overextension; H canc, H cancellation task; LE, left extension; LE/RE, ratio of left-right extension; N+, neglect patients; N-, non-neglect patients; PB Land-M, perceptual bias on Landmark motor task; PB Land-V, perceptual bias on Landmark verbal task; RB Land-M, response bias on Landmark motor task; RB Land-V, response bias on Landmark verbal task; RE, right extension. (shrink)