The law requires every member state to give university places to EU students on the same terms as their own nationals. Because education is devolved in the UK, Scotland can charge English students tuition fees – because they are not treated by the EU as non-UK citizens – while giving Scottish students free tuition.
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Dennis Abbott, Vassiliou's spokesman, said that it would illegal if the Scottish government were to have a service charge but then pay that charge for all Scottish students.
"It would be discrimination if Scotland introduced service charges: they would have to be paid by all EU students, which would mean Scottish students as well," he told BBC Radio Scotland.
Maintenance grants, however, would fall outside EU law. "If the Scottish government idea is somehow to ensure that Scottish students and resident students get the best possible deal, that might be a way of doing it," he added.
Introducing barriers to make it more difficult for European students to study in Scotland conflicted with the EU's main ethos, Abbott said. "The EU wants to encourage young people to study abroad: we want Scottish students to have the opportunity to study in France, Germany and Austria and other European countries, where they shouldn't be treated as second-class citizens. And we don't want EU students who come to Scotland to be treated as second-class citizens."