Non EU students were not affected by last year's fee changes but they generally pay higher fees, set directly by the institution they attend.
This broke down to a 6% rise in students from other European Union countries (total of 112, 150 in 2008) and a 4% rise in those from non EU countries (total 229, 640).
Mrs May expects her new measures to cut non-EU student numbers by at least 70, 000-80, 000 a year, or more than a quarter of the non-EU total (EU citizens don't need visas to study in Britain), though both numbers and policy details remain a work in progress.
Similarly, non-EU or non-US carriers that have landing rights in the EU or US must abide by local travellers' rights regulations.
MEPs were joined in the session by parliamentarians from national parliaments from EU and non-EU member states.
The Schengen zone covers 22 EU states and three non-EU countries - Iceland, Norway and Switzerland.
The deal also let EU airlines operate flights between the US and other non-EU countries, and made it easier for airlines to enter into code sharing agreements and other types of alliances.
It has been applying the EU emissions law to all airlines since then, despite protest from most non-EU countries.
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Customs officers said non-EU nationals coming to the island and "engaging in musical activity" needed approval.
Other questioners focused on police administration, the non-EU work migrants cap and alcohol-related anti-social behaviour.
German leaders are seeking help from the U.S. Federal Reserve and other non-EU central banks, too.
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We are controlling legal immigration - having introduced a cap on non-EU economic migrants.
Mrs May announced a temporary cap on non-EU immigration last month ahead of a permanent limit next year.
Turkey wants non-EU NATO members, such as itself, assured of closer participation than the EU aims to grant.
"Bringing non-EU nationals into the UK doesn't always flow as smoothly as you'd wish, " said a Widnes spokesman.
The president will fly to non-EU state Norway and then visit Finland, Austria, Belgium and Italy, say officials.
But by far the biggest route for non-EU entrants into this country has been the student visa route.
This is a pipe-dream, if only because NATO's membership includes such non-EU countries as Canada, Norway and Turkey.
Motorists wanting to exchange non-EU licences must now prove they have passed a test in a designated country.
The U.S., Turkey, Serbia, China and Russia were the biggest non-EU source countries.
That would make him an illegal immigrant, liable to the same rapid expulsion as an extracomunitario (ie, non-EU citizen).
This means even deeper cuts to non-EU net-migration are necessary to reach the target of the tens of thousands.
Sir Andrew also said the government's points-based system to control non-EU immigration had so far "had very little effect".
The university's licence to sponsor non-EU students was controversially revoked in August last year, leaving hundreds of students without courses.
Admissions body Ucas said the number of non-EU applicants had risen 24.7%, with applications from the EU going up 6%.
Ms Reding cited examples where data could be shared with non-EU countries, such as data transfer between competition or customs authorities.
Although Greece, Romania and Lithuania have yet to sign up to the findings, non-EU states Croatia and Liechtenstein have done so.
For example, citizens of non-EU countries cannot hold dual citizenship, which they are able to do in France and the Netherlands.
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Ministers say all non-EU prisoners convicted of serious drug or gun crimes are now considered for deportation, irrespective of the length of their sentence.
Passengers on non-EU carriers leaving from an EU airport are also covered.
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