This article describes the field of human-artifact interaction to develop “timeaxis design”from a semiotic viewpoint. I focus especially on narratology and ludology for considering the subject, and discuss the structure of dynamics of time flow in the field of narrative and game in design. (1) Narratology and ludology offer some effective concepts for interaction design as well as game. (2) Personalized (informal) time is significant in defining timeaxis in interaction. (3) Time in the course of interaction is nonlinear and polychronic. (4) Chronomic factors are necessary in considering reality and agency in interaction.