Recurrent claims of ineffable experience and their importance for communication theory are analyzed in this paper. Four positions are identified: (1) the "complete effability/complete communicability" position is historically identified with Western culture but repudiated by modern thought; (2) the "complete ineffability/complete communicability" position has some adherents but is self-defeating; (3) the "complete effability/limited communicability" position provides the conceptual base for most of the work in twentieth-century communication theory; and (4) the "complete ineffability/limited communicability" position has consistent support but requires a new form of theory which differentiates "coordination" and "consubstantiation" as genres. The paper points out that explication of the features of situations which prompt recognition of ineffability and the characteristics of individual and cultural attempts to express the ineffable necessitate a reanalysis of the function of several social institutions, and that this analysis suggests new directions for the development of communication theory. (Author/RL)