One challenge of learning a foreign language (L2) in adulthood is the mastery of syntactic structures that are implemented differently in L2 and one's native language (L1). Here, we asked how L2 speakers learn to process syntactic constructions that are in direct conflict between L1 and L2, in comparison to structures without such a conflict. To do so, we measured EEG during sentence reading in three groups of German learners of Dutch with different degrees of L2 experience (from 3 to more than 18 months of L2 immersion) as well as a control group of Dutch native speakers. They read grammatical and ungrammatical Dutch sentences that, in the conflict condition, contained a structure with opposing word orders in Dutch and German (sentence-final double infinitives) and, in the no-conflict condition, a structure for which word order is identical in Dutch and German (subordinate clause inversion). Results showed, first, that beginning learners showed N400-like signatures instead of the expected P600 for both types of violations, suggesting that, in the very early stages of learning, different neurocognitive processes are employed compared with native speakers, regardless of L1–L2 similarity. In contrast, both advanced and intermediate learners already showed native-like P600 signatures for the no-conflict sentences. However, their P600 signatures were significantly delayed in processing the conflicting structure, even though behavioral performance was on a native level for both these groups and structures. These findings suggest that L1–L2 word order conflicts clearly remain an obstacle to native-like processing, even for advanced L2 learners.