The present study analysed task-dependent effects on the exploratory behaviour of neglect patients during their spontaneous search of the surroundings. We were asking whether different tasks would be associated with different structuring of the visual display and, therefore, would result in different forms of neglect in one and the same brain-damaged subjects. Neglect patients' eye and head movements were recorded when they searched for a target within a homogeneous stimulus array surrounding the subjects. Subsequently, they explored the same array which was now segmented into different areas. When the patients' attention was allocated to the whole surrounding space, all patients completely neglected the left hemispace and spontaneously attended to the right hemispace. No significant left-right asymmetry was detected in a selected segment located in the periphery of the attended, right hemispace. However, all patients completely ignored the left part of this segment when they had to concentrate visual search on this segment alone. The results suggest an important influence of task-dependent effects on the exploratory behaviour of neglect patients. They show that one and the same physical stimulus at one and the same location in a scene might be attended or, in another situation, neglected, just depending on the behavioural goal of the subject. The findings support the idea that the brain organises and reorganises continuously the representation of the same physical input according to the changing task requirements.