We examined the effect of word stress position on bilingual auditory cognate processing. Turkish–Dutch early bilinguals who are dominant in their L2 (Dutch) performed an auditory lexical decision task in Turkish or Dutch. While Dutch has variable word stress, with a tendency for penultimate stress, stress in Turkish is mostly predictable and usually falls on the ultimate syllable. Our tasks included two-syllable cognates with penultimate stress in both languages, ultimate stress in both languages, or ultimate stress in Turkish and penultimate stress in Dutch. Some cognate facilitation effects arose in Dutch, while inhibition was found in Turkish. Cognates with ultimate stress were processed faster than cognates with penultimate stress, in both languages. This shows that in Turkish–Dutch early bilinguals, cognate processing depends on Turkish stress position, although Dutch is dominant. Together, the findings support the view that cognates have separate, though linked representations.