Lesion studies of the parietal cortex have led to a wide range of conclusions regarding the coordinate reference frame in which hemineglect is expressed. A model of spatial representation in the parietal cortex has recently been developed in which the position of an object is not encoded in a particular frame of reference, but instead involves neurons computing basis functions of sensory inputs. In this type of representation, a nonlinear sensorimotor transformation of an object is represented in a population of units having the response properties of neurons that are observed in the parietal cortex. A simulated lesion in a basis–function representation was found to replicate three of the most important aspects of hemineglect: (i) the model behaved like parietal patients in line–cancellation and line–bisection experiments; (ii) the deficit affected multiple frames of reference; and (iii) the deficit could be object–centred. These results support the basis–function hypothesis for spatial representations and provide a testable computational theory of hemineglect at the level of single cells.