This paper suggests the independence of grammaticalization and pragmaticalization processes. These two processes are originally and self-evidently autonomous evolutionary paths that occur independently of each other. However, grammaticalization is often discussed, indeed in the majority of the recent studies, in correlation to some unidirectional features that co-occur with grammaticalization. Such features include, structurally, for example, “bondedness” and “structural scope”, and functionally, for example, “increase in abstraction” and “pragmaticalization”. These unidirectional features are at times even considered too authoritatively criterial to judge a given language change as an instance of grammaticalization. This study illustrates a piece of evidence for the asymmetric relationship of grammaticalization and pragmaticalization. That is, the two groups of Japanese discourse markers — (1) demo type connectives and (2) na elements — experience quite different historical changes. The group (1) undergoes both grammaticalization and pragmaticalization, but the group (2) undergoes pragmaticalization without involving grammaticalization.