Grammaticalization is the process whereby lexical or content words acquire grammatical function or existing grammatical units acquire further grammatical functions. Grammaticalization has received a great deal of attention within cognitive linguistics, because it is characterized by interwoven changes in the form and meaning of a given construction and can therefore be seen as a process that is essentially grounded in meaning. Polysemy of /gada/ in Korean and /paj/ in Thai have both similarities and differences and main reason of the similarities come from the fact that the two words have the same prototypical meaning. Then the meaning extended from the movement of animate to non-animate agents, from the movement of concrete to abstract trajectors, from objective motion to subjective motion, and lastly from spatial meaning to temporal/aspectual meaning by grammaticalization process. Both words have aspectual meaning of continuation (imperfective aspect), while /paj/ in thai have the meaning of perfective aspect which /gada/ in Korean does not have. There still is a controversy on the issue of grammaticalization especially in Thai academia, but I suggest that phenomenon of content word such as /gada/ in Korean and /paj/ in Thai acquiring additional function as auxiliary verbs with aspectual meaning should be considered as a kind of grammaticalization. Though we cannot bring to a conclusion that how far the words are grammaticalized at the moment, but it is still very interesting and valuable to study the grammaticalization which might let us predict the trend of language change.