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As has been noted, those born in Mexican territory are citizens of Mexico, regardless of the nationality of their parents.
The Mexican nationality law acknowledges that a Mexican by birth may possess another nationality. If that is the case, however, such an individual must always enter and leave the country as a Mexican (by presenting a Mexican proof of citizenship).
Mexico actively encourages dual citizenship (Doble Nacionalidad) and US/Mexican nationals should carry citizenship documentation for both countries when traveling to Mexico.
Timatic, the database used by airlines, lists the what Mexican documents are acceptable if you don't have a Mexican passport: