This paper examines the process of acquiring L2s that are closely related to the L1 through data on how adult French speakers learning L2 Spanish in a formal setting develop knowledge and use of past tenses in this L2. We consider the role of transfer and simplification in acquiring mental representations of the L2 grammar, specifically in the area of tense and aspect, and how learners deal with integrating grammatically encoded, lexical and discursive information, including mismatching feature combinations leading to particular inferential effects on interpretation. Data is presented on the Spanish past tenses (simple and compound past, pluperfect, imperfect and progressive forms) from two tasks, an oral production film retell and a multiple-choice interpretation task, completed by learners at A2, B1, B2 and C1 CEFR levels (N = 20-24 per level). L1 influence is progressively attenuated as proficiency increases. Difficulties were not always due to negative L1 transfer, but related also to grammar-discourse interface issues when integrating linguistic and pragmatic information in the interpretation process. This has clear implications for the teaching of closely related languages: instruction should not only focus on crosslinguistic contrasts, but also prioritize uses requiring complex interface integration, which are harder to process.