It is often assumed that language is supported by domain-specific neural mechanisms, in part based on neuropsychological data from aphasia. If, however, language relies on domain-general mechanisms, it would be expected that deficits in non-linguistic cognitive processing should co-occur with aphasia. In this paper, we report a study of sequential learning by agrammatic aphasic patients and control participants matched for age, socio-economic status and non-verbal intelligence. Participants were first exposed to strings derived from an artificial grammar after which they were asked to classify a set of new strings, some of which were generated by the same grammar whereas others were not. Although both groups of participants performed well in the training phase of the experiment, only the control participants were able to classify novel test items better than chance. The results show that breakdown of language in agrammatic aphasia is associated with an impairment in artificial grammar learning, indicating damage to domain-general neural mechanisms subserving both language and sequential learning. (Contains 3 tables and 1 figure.)