Being a dual national and carrying the passport of two countries is perfectly legal. Under U.S. law, naturalizing as a citizen of a foreign state will not in and of itself cause you to lose your U.S. citizenship. General information about dual nationality is available on the Department of State website Dual Nationality section.
The naturalization process in Mexico is managed by the Secretaría de Relaciones Exteriores (SRE). There are several methods of naturalizing in Mexico. Generally, Mexican nationality can be acquired by meeting various residency, family, or marriage requirements. Please contact SRE’s main officefor more information on the application procedure.
The Mexican government is encouraging those who are eligible to become dual US-Mexican citizens. Mexico believes the effort will benefit both countries.
Source: Mostly by way of Texas Public Radio