In the field of neurodegeneration, speech and language assessments are useful for diagnosing aphasic syndromes and for characterizing other disorders. As a complement to classic tests, scalable and low-cost digital tools can capture relevant anomalies automatically, potentially supporting the quest for globally equitable markers of brain health. However, this promise remains unfulfilled due to limited linguistic diversity in scientific works and clinical instruments. Here we argue for cross-linguistic research as a core strategy to counter this problem. First, we survey the contributions of linguistic assessments in the study of primary progressive aphasia and the three most prevalent neurodegenerative disorders worldwide-Alzheimer's disease, Parkinson's disease, and behavioural variant frontotemporal dementia. Second, we address two forms of linguistic unfairness in the literature: the neglect of most of the world's 7000 languages and the preponderance of English-speaking cohorts. Third, we review studies showing that linguistic dysfunctions in a given disorder may vary depending on the patient's language and that English speakers offer a suboptimal benchmark for other language groups. Finally, we highlight different approaches, tools and initiatives for cross-linguistic research, identifying core challenges for their deployment. Overall, we seek to inspire timely actions to counter a looming source of inequity in behavioural neurology.