Persons with aphasia (PWA) experience differences in attention after stroke, potentially impacting cognitive/language performance. This secondary analysis investigated physiologically measured vigilant attention during linguistic and nonlinguistic processing in PWA and control participants. To evaluate performance and attention in a language task, seven PWA read sentences aloud (linguistic task) and were compared to a previous data set of 10 controls and 10 PWA. To evaluate performance and attention in a language-independent task, 11 controls and nine PWA completed the Bivalent Shape Task (nonlinguistic task). Continuous electroencephalogram (EEG) data were collected during each session. A previously validated EEG algorithm classified vigilant-attention state for each experiment trial into high, moderate, distracted, or no attention. Dependent measures were task accuracy and amount of time spent in each attention state (measured by the number of trials). PWA produced significantly more errors than controls on the linguistic task, but groups performed similarly on the nonlinguistic task. During the linguistic task, controls spent significantly more time than PWA in a moderate-attention state, but no statistically significant differences were found between groups for other attention states. For the nonlinguistic task, amount of time controls and PWA spent in each attention state was more evenly distributed. When directly comparing attention patterns between linguistic and nonlinguistic tasks, PWA showed significantly more time in a high-attention state during the linguistic task as compared to the nonlinguistic task; however, controls showed no significant differences between linguistic and nonlinguistic tasks. This study provides new evidence that PWA experience a heightened state of vigilant attention when language processing demands are higher (during a linguistic task) than when language demands are lower (during a nonlinguistic task). Collectively, results of this study suggest that when processing language, PWA may allocate more attentional resources than when completing other kinds of cognitive tasks.