New Mexico UK /njuː mɛk.sɪ.kəʊ/US /nu ˈmɛk.sɪ.koʊ/ noun5 •A state in the southwestern United States. Capital: Santa Fe. Largest city: Albuquerque. •A former provincial kingdom in New Spain. •A former territory of Mexico. •A former transitional government in the United States. •A former territory of the United States.