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Note that you can find many other payment modules on Addons: http://addons.prestashop.com/en/4-payments-gateways.
Adyen
Adyen is a global payment company leading the way in defining a new generation of payment services. Built from the ground up on cutting-edge technology, its global payment platform enables businesses to accept payments from anywhere in the world using the same technical platform and administrative back office interface. It supports all relevant sales channels, including online, mobile and Point-of-Sale (POS), and can process 224 different payment methods and 187 transaction currencies used across six continents. Meeting the highest standards of security and stability, the Adyen payment platform is certified PCI Level 1.
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Once the settings are in place, your customers will see the "PayPal" option appear in the shop's front-office as part of the available payment methods.
Realex
Realex Payments processes payments in excess of £18 billion per annum for over 12,500 online retailers, including some of the world’s leading brands – Vodafone, Aer Lingus, Virgin Atlantic, Paddy Power, Chain Reaction Cycles, AA, 32Red, notonthehighstreet.com to name a few.
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