Arithmetical reasoning ability has been investigated in a group study of patients with unilateral cerebral lesions. Two series of 38 and 39 patients, who had suffered unilateral cerebral lesions of the right and left cerebral hemisphere, respectively, were investigated. They completed a neuropsychological battery that included a test of computation (Graded Difficulty Arithmetic, GDA; Jackson & Warrington, 1986), and a new test of numerical series completion (Arithmetical Reasoning Test, ART). Whereas the left-hemisphere lesion group were markedly more impaired on the GDA compared to both the right-hemisphere lesion group and a standardization sample, both lesion groups were equally severely impaired on the ART. It is suggested that the abstraction of numerical relations, which is essential to numerical series completion, relies on the integrity of the right hemisphere. A global model of arithmetic processing that incorporates these findings is proposed. (JINS, 1997, 3, 260–268.)