Event-related potentials (ERPs) are used to study how language is processed in the brain, including differences between native (L1) and second-language (L2) processing. A P600 ERP effect can be measured in proficient L2 learners in response to an L2 syntactic violation, indicating native-like processing. Cross-language similarity seems to be a factor that modulates P600 effect size. This manifests in a reduced P600 effect in response to a syntactic violation in the L2 when the syntactic feature involved is expressed differently in two languages. We investigate if this reduced P600 effect can be explained by assuming that ERPs reflect learning signals that arise from mismatches in predictive processing; and in particular that the P600 reflects the error that is back-propagated through the language system (Fitz & Chang, 2019). We use a recurrent neural network model of bilingual sentence process-ing to simulate the P600 (as back-propagated prediction error) and have it process three types of syntactic constructions differing in cross-language similarity. Simulated English-Spanish participants displayed a P600 when encountering constructions that are similar between the two languages, but a reduced P600 for constructions that differ between languages. This difference between the two P600 responses mirrors what has been observed in human ERP studies. Unlike human participants, simulated participants showed a small P600 response to constructions unique to the L2 (i.e., grammatical gender), presum-ably because of how this grammatical feature is encoded in the model. Our modelling results shed further light on the viability of error propagation as an account of ERPs, and on the effects of syntactic transfer from L1 to L2.