New figures show Scottish universities received 17,787 applications from the EU by the January deadline, compared to just 5941 in 2008. Numbers are up more than 5% on 2012 alone.
The rise is important because EU students compete for the same places as Scots and the estimated £75 million cost of educating them is the responsibility of the Scottish taxpayer.
Last night, UCU Scotland, which represents lecturers, issued a warning over the figures.
"The continued increase in applications from EU students is particularly worrying as any increase will result in fewer places for Scots at a time when universities are already meeting their quota," said a spokesman.
"While we welcome a diverse mix. We need to consider ways to reduce the number of EU students coming to Scotland simply to avoid fees."
Overall, the figures from the Universities and Colleges Admissions Service (Ucas) show more potential students than ever before are now trying to get into university.
The number of Scots applying has risen by 2.1% to 39,358, including a welcome increase in applicants from poorer backgrounds.
The number of students from England applying to Scotland has risen by nearly 15% to more than 28,000, despite the fact they now pay fees of up to £9000 a year to attend courses.
However, numbers are still below 2011 levels, when more than 30,000 applied, and these students do not compete for the same places as Scots.
Michael Russell, the Education Secretary, welcomed the record numbers of Scottish applicants.He said: "I am particularly pleased to see that more school-leavers from deprived areas are applying.
"I have already announced an extra 2000 higher education places for next year, targeted at those progressing from college and students from deprived areas, and I am confident Scottish applicants will be able to achieve their goals."
The figures were also welcomed by Robin Parker, president of NUS Scotland, although he warned against universities "cashing in" on students from the rest of the UK.
However, opposition politicians seized on the additional pressure created by the EU student figures.
Mr Russell has already raised the prospect of a service charge for EU students to redress the balance, but there has been little progress so far.
Hugh Henry, Scottish Labour's education spokesman, said the increase in EU student numbers would mean more subsidies from the Scottish budget and, therefore, cuts elsewhere.
Liz Smith, the Scottish Tories' education spokeswoman, added: "There are financial implications associated with the rising number of EU applications."
However, a Scottish Government spokeswoman said the number of EU students accepted on to courses would be about half the number of applicants. She said: "We are funding a record number of places and will continue to liaise with universities to deliver opportunities for Scottish students.
"We are also continuing to examine how we could raise additional income from students from outside Scotland, within EU law."
Alastair Sim, director of Universities Scotland suggested EU students were not only being motivated by cost, but also the quality of Scottish higher education.
He said: "EU student behaviour is not motivated by price alone, but on a range of factors including the value of the educational offer, institutions' commitment to employability and the quality of the student experience."