In this study, I first examine what criteria have been raised since the beginning of language studies, to affirm that the languages of other nations were of the same lineage or the same root language. Then, I examine what kind of criticism has been made about the comparative study between Korean and other languages, especially Mongolian. According to the opinions raised by linguists, to affirm that two languages would be derived from the same lineage or from the same root, it is necessary not only the coincidence of the basic words but also that of nouns, predicates, phonological rules and morphemes. Naturally, both languages should have in common the same grammar rule in the process of combining morphemes. I next examine the nominal phrases of Nahuatl, the indigenous language of Mexico, and of the Korean language, analyzing them in morphemes and comparing them, in order to confirm that the noun phrases coincide in their pronunciation and meaning. In this process, I have confirmed that in both languages the basic words are coincided, such as 'moon', name of a natural object, and 'foot', name of a part of the human body. Especially, through morphological analysis, I have come to know that Nahuatl shares the phonological rule with Korean, that is, the intrinsic grammar of Korean as the use of morpheme 'n' in the process of the combination of morphemes. I could also confirm that there is a coincidence of the personal pronouns between both languages, and see that there are also the nominative case particles '이 (i)' and ' 가 (ca)' of Korean in Nahuatl. And both languages have several identical predicates in common. It will be very important that the ancient words or dialects like 'colhua / coli' of Nahuatl and '골회 (colhue) / 고리 (coli)' of Korean have coincided, because that would mean that both languages do not only have a mere coincidence of some words but also, with more importance, that of the ancient dialects.