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The online authorization you mentioned is the Electronic Authorization System (SAE) or electronic visa which allows Russian, Ukrainian and Turkish citizens to obtain an electronic authorization to travel to Mexico without a consular visa. According to the website of Mexican Embassy in Turkey it's free:
- The electronic visa (SAE) is available only for Holders of Turkish ordinary (BORDO) passports.
- Holders of Turkish special (green) and service (grey) passports must apply in the nearest consular office of Mexico for the corresponding stamped visa.
- The electronic visa (SAE) is valid for 30 days since issuing date and a single entry. The holders could stay for a period up to 180 days*.
- The electronic visa (SAE) is FREE. Do not accept charges to obtain it.
- The electronic visa (SAE) is available only if you are traveling by air with an airline incorporated to SAE. If you want to entry by land or by sea, it is necessary to apply for a visa in the nearest consular office of Mexico.
At the point of entry, the migratory agent will require the following documentation:
- FMM form dully filled
- Hotel bookings in Mexico and return or onward flight ticket.
- Documents proving the purpose of the trip (tour itinerary, company invitations, company contract, etc)
- Proof of financial means.