Yes, you must remove the car from Mexico eventually; unless you manage to nationalize it, a difficult and rather expensive process, which the government seems to be curtailing.
When you bring your car to Mexico, you do so on an 'Importada Temporal' (Temporary Importation) and you have signed and posted a bond with your credit card guaranteeing that you will remove the vehicle from Mexico whenever your immigration status ends. You may not ever sell that vehicle in Mexico; not even for parts if you wreck it. Should you do so illegally, and should the car ever be used in a crime, cause damage or kill someone, you would be traced through the VIN and remain responsible; even though it might have been sold ten times over. Mexican jails and prisons aren't nice. In fact, if your car is stolen you will still face those same problems and cannot ever bring a replacement into Mexico. That's the way it is and that's what you agree to when you bring your car to Mexico and sign on the dotted line. So, if you intend to remain in Mexico 'forever' and don't want the possible problem of having to remove an aged wreck from the country by truck, you might want to consider not bringing a foreign plated vehicle to Mexico and buying a car here. There are dealers in all of the major cities for new models as well as reliable used cars with good titles.

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Read "Streets of Glass" to discover the experience of a retired couple's permanent move to Lake Chapala, Jalisco, Mexico.
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