The relational concepts developed in mathematics and psychology are used in this paper to explicate the needs and responsibilities of dramatic acting and theatre research. A parallel is constructed between the emergence of the mathematical concept of function, the awakening of psychology to the concept of relationship (especially regarding family counseling), and the functional relationships of actors dramatizing situations before audiences. Descriptions of developments in family counseling show the therapeutic effects of psychodrama and how actors can learn from such family counseling procedures. It is proposed that actors are a part of society who simulate the lives of other members of society for the benefit (understanding) of society as a whole. This approach to drama based on systems theory should stimulate new ideas about acting and renewed enthusiasm for theatre research. (RL)