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It's not a surprise you cannot find application for a Continental Airlines credit card because this airline was acquired by United Airlines. Continental's frequent flyer program turned into MileagePlus and all credit cards were transferred as well. So now you have to choices: you can apply for a United Airlines credit card or you can apply for a travel rewards credit card. While everything is quite clear about the first card, the second may need some additional information. Travel rewards credit cards are cards that are not tied to one specific airline. Such cards will allow you to earn rewards on all your purchases, including on travel purchases, and redeem them for travel expenses like airfare, hotel stays, and rental cars.