جزر كوك ← جزر كايمان: تأشيرة سياحية قصيرة المدة

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You don't need a visa to visit the Cayman Islands as a tourist. The CBC country list has no row for your territory by name, but its New Zealand row ("including Associated States and Overseas Territories") says it includes territories like yours, and that row is under "Visa Not Required". If you are unsure whether it covers your passport, ask CBC before you travel. The CBC says visitors may be granted permission to land for up to six months (this can be extended on application), and the officer decides your permitted stay on arrival. On arrival you still need a passport or other valid travel document that is valid beyond your return ticket date, and a paid-up return or onward ticket. The officer may also ask you to show you have enough money for your stay, and can refuse entry on other grounds.

المصدر: Cayman Islands Government, Customs & Border Control: List of Countries - Visa Required (the page shows no date)