A controversial issue in the field of language development is whether language emergence and growth is dependent solely on processes specifically tied to language or could also depend on basic cognitive processes that affect all aspects of cognitive competence (domain-general processes). The present article examines this issue using a large battery of infant information-processing measures of memory, representational competence, processing speed, and attention, many of which have been shown to predict general cognition in a cohort of full-terms and preterms. Results showed that various aspects of infant memory and representational competence (a) related to language at both 12 and 36 months, (b) predicted similarly for the two groups, and (c) predicted 36-month language, independently of birth status, 12-month language, and the 12-month Bayley Mental Development Index. Additionally, the results established predictive validity for the MacArthur 12-month language measure. These findings support a domain-general view of language.