.eu is the country code top-level domain (ccTLD) for the European Union. Any individual or company can register a .eu domain as long as they comply with one of the following categories;

Undertaking having its registered office, central administration or principal place of business in the EU.

Organisation established within the Community without prejudice to the application of national law.

Natural person resident within the EU Community.

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Domainmonster.com Customer Support Team.
Domain Name Registration Information & Resources.