This article has two main objectives. First, we offer an introduction to the subfield of generative third language (L3) acquisition. Concerned primarily with modeling initial stages transfer of morphosyntax, one goal of this program is to show how initial stages L3 data make significant contributions toward a better understanding of how the mind represents language and how (cognitive) economy constrains acquisition processes more generally. Our second objective is to argue for and demonstrate how this subfield will benefit from a neuro/psycholinguistic methodological approach, such as event-related potential experiments, to complement the claims currently made on the basis of exclusively behavioral experiments.