This study explores the contribution of nonverbal working memory and processing speed on bilingual children’s morphosyntactic knowledge, after controlling for language exposure. Participants include 307 Spanish–English bilinguals in Kindergarten, second, and fourth grade (mean age = 7;8, SD = 18 months). Morphosyntactic knowledge in English and Spanish was measured using two separate language tasks: a cloze task and a narrative language task. In a series of four hierarchical linear regressions predicting cloze and narrative performance in English and Spanish, we evaluate the proportion of variance explained after adding (a) English exposure, (b) processing speed and working memory, and (c) interaction terms to the model. The results reveal the differential contribution of nonverbal cognitive skills across English and Spanish. Cognition was not significantly related to performance on either grammatical cloze or narrative tasks in Spanish. Narrative tasks in English were significantly predicted by processing speed, after controlling for age and exposure. Grammatical cloze tasks in English posed an additional cognitive demand on working memory. The findings suggest that cognitive demands vary for bilinguals based on the language of assessment and the task.