Eye gaze plays an important role in human communication. One foundational skill in human social interaction is joint attention which is receiving increased interest in particular in the area of human-agent or human-robot interaction. We are focusing here on patterns of gaze interaction that emerge in the process of establishing joint attention. The approach, however, should be applicable to many other aspects of social communication in which eye gaze plays an important role. Attention has been characterized as an increased awareness 1 and intentionally directed perception 2 and is judged to be crucial for goal-directed behavior. Joint attention can be defined as simultaneously allocating attention to a target as a consequence of attending to each other's attentional states 3. In other words: Interlocutors have to deliberatively focus on the same target while being mutually aware of sharing their focus of attention 2 4.