Large credit card companies nearly all compete in the global marketplace. Most major cards are accepted in foreign countries. While there are often hefty fees for using a credit card in a foreign country, this can be avoided by taking out a credit card whose headquarters are in said country.
Research companies in the country. Many large banking institutions, like HSBC Bank, have international offices in over 200 countries. Some companies are local only to that particular country. It is easier to obtain a foreign credit card through a large bank.
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Research the currency in the country. To complete a foreign credit application, you'll need to be able to convert dollars to the currency. To make things easier, convert your income in terms of annual salary, monthly salary and weekly salary.
Contact individual banks and finance companies abroad via email. You want to give them a heads-up that you'll be applying. This may expedite matters. You'll need to provide your social security number for credit verification and if the lender knows that you are a foreigner, she will know to access the American credit bureaus.
Apply at your selected companies. Fill out the applications completely. If you run into problems on the application, make sure to contact the bank or lender. You may want to get a post office box in the foreign country so you'll have local address.
Submit the applications to the bank or lender. Make sure to review all offers with a trusted adviser, like a family accountant or lawyer.