Ah, yes. 'Better' Together's latest favourite scare-story.
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Yes, the fact is they would most likely need to re-apply for membership. This isn't
defininte-- certainly, arguments would be made that existing membership should stand. It might work, it might not.
As for re-admission, obviously there's lots of sabre-rattling by, among others, Spain. Actually...pretty much Spain (and Westminster, of course). The reality, though is that there's virtually no chance that Scotland would actually be denied membership.
http://www.scottishglobalforum.net/scottish-independence-and-eu-membership-debunking-the-myths.htmlAs far as it goes, I would say there's more chance of ending up outside the EU if Scotland remains dependent. After all, the government are promising an EU referendum by 2017, and the way opinion polls are skewing, I'd say there's a greater probability of South/Middle England voting to drag us all out of the EU, than of the EU denying membership to an independent Scotland.