Cognates’ cross-linguistic formal similarity causes them to be more activated than non-cognates. Based on the Modular Online Growth and Use of Language framework (Sharwood Smith & Truscott, 2014, The Multilingual Mind: A Modular Processing Perspective, Cambridge University Press), the stronger activation of cognates compared to non-cognates should spread to any L2 structures containing them, leading to greater syntax learning. This should occur for cross-linguistically dissimilar structures but not for cross-linguistically similar ones, processed using L1 syntax. In Experiment 1, two groups of Spanish natives learnt Spanish–Basque non-cognate nouns and cognate or non-cognate verbs. Then, they were exposed to L2 structures dissimilar to Spanish via sentence–picture pairs. A picture-description task with non-cognates tested syntax learning. In Experiment 2, the learning targets were L2 structures similar to Spanish. Exposure to the structures with cognates, as opposed to non-cognates, resulted in greater learning only in Experiment 1. From this, we conclude that cognates facilitate L2 syntax acquisition, but only when the structures cannot be processed using the native language.