It is increasingly acknowledged that, often, patients with post-stroke aphasia not only have language impairments but also deficits in other cognitive domains (e.g. executive functions) that influence recovery and response to therapy. Many assessments of executive functions are verbally based and therefore usually not administered in this patient group. However, the performance of patients with aphasia in such tests might provide valuable insights both from a theoretical and clinical perspective. We aimed to elucidate (i) if verbal executive tests measure anything beyond the language impairment in patients with chronic post-stroke aphasia, (ii) how performance in such tests relates to performance in language tests and nonverbal cognitive functions, and (iii) the neural correlates associated with performance in verbal executive tests. In this observational study, three commonly used verbal executive tests were administered to a sample of patients with varying aphasia severity. Their performance in these tests was explored by means of principal component analyses, and the relationships with a broad range of background tests regarding their language and nonverbal cognitive functions were elucidated with correlation analyses. Furthermore, lesion analyses were performed to explore brain–behaviour relationships. In a sample of 32 participants, we found that: (i) a substantial number of patients with aphasia were able to perform the verbal executive tests; (ii) variance in performance was not explained by the severity of an individual’s overall language impairment alone but was related to two independent behavioural principal components per test; (iii) not all aspects of performance were related to the patient’s language abilities; and (iv) all components were associated with separate neural correlates, some overlapping partly in frontal and parietal regions. Our findings extend our clinical and theoretical understanding of dysfunctions beyond language in patients with aphasia.