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A little reading 

Gibraltar is a British overseas territory located near the southernmost tip of the Iberian Peninsula and overlooking the Strait of Gibraltar, sharing a border with Spain to the north. It is part of the EU, having joined the European Economic Community under the United Kingdom in 1973. Article 355(3) (ex Article 299(4)) applies the treaty to "the European territories for whose external relations a Member State is responsible", a provision which in practice only applies to Gibraltar. Although it is part of the EU, Gibraltar is outside the customs union and VAT area and is exempted from the Common Agricultural Policy; it does not form part of the Schengen Area.[47] As a separate jurisdiction to the UK, Gibraltar's government and parliament are responsible for the transposition of EU law into local law



Yes you can move to Gibraltar with only an EU passport, but like most places work is limited and accommodation is very expensive

From your question I do not understand your user name ??    alexfromgibraltar ?????????

Thank  You  ever  so  much !

(moderated: inappropriate comment)