Several studies in the area of third language acquisition (L3A) have considered various factors influencing this process, but the effect of language dominance has not been thoroughly examined. The main goal of this study is to investigate whether the acquisition of relative clauses (RCs) in L3 English is influenced by language internal factors, such as the syntactic features of the target language, or by external factors in the form of cross-linguistic influence (CLI). A total of 90 participants (40 Spanish-dominant, 40 Basque-dominant, 10 L1 Spanish-L2 English) and 10 native speakers of English completed a production and a comprehension task. Findings show that the L3 learners’ production of RCs seems to be driven by language internal factors, whereas their comprehension appears to be influenced by their previously acquired languages, mainly by Spanish. It is concluded that neither language dominance nor other traditionally considered factors play a determinant role in the acquisition of RCs in L3 English by these participants.