We considered the role of orthography and task-related processing mechanisms in the activation of morphologically related complex words during bilingual word processing. So far, it has only been shown that such morphologically related words (i.e., morphological family members) are activated through the semantic and morphological overlap they share with the target word. In this study, we investigated family size effects in Dutch-English identical cognates (e.g., tent in both languages), non-identical cognates (e.g., pil and pill, in English and Dutch, respectively), and non-cognates (e.g., chicken in English). Because of their cross-linguistic overlap in orthography, reading a cognate can result in activation of family members both languages. Cognates are therefore well-suited for studying mechanisms underlying bilingual activation of morphologically complex words. We investigated family size effects in an English lexical decision task and a Dutch-English language decision task, both performed by Dutch-English bilinguals. English lexical decision showed a facilitatory effect of English and Dutch family size on the processing of English-Dutch cognates relative to English non-cognates. These family size effects were not dependent on cognate type. In contrast, for language decision, in which a bilingual context is created, Dutch and English family size effects were inhibitory. Here, the combined family size of both languages turned out to better predict reaction time than the separate family size in Dutch or English. Moreover, the combined family size interacted with cognate type: the response to identical cognates was slowed by morphological family members in both languages. We conclude that (1) family size effects are sensitive to the task performed on the lexical items, and (2) depend on both semantic and formal aspects of bilingual word processing. We discuss various mechanisms that can explain the observed family size effects in a spreading activation framework.