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This paper provides new evidence on how the presence of immigrant peers in the classroom affects native student achievement. The analysis is based on longitudinal administrative data on two cohorts of vocational training students in Italy's largest region. Vocational training institutions provide the ideal setting for studying these effects because they attract not only disproportionately high shares of immigrants but also the lowest ability native students. We adopt a value added model, and exploit within-school variation both within and across cohorts for identification. Our results show small negative average effects on maths test scores that are larger for low ability native students, strongly non-linear and only observable in classes with a high (top 20%) immigrant concentration. These outcomes are driven by classes with a high average linguistic distance between immigrants and natives, with no apparent role played by ethnic diversity.