The influence of communication processes on group outcomes is discussed from two perspectives, one in which influence does not exist and one in which influence is central. Formal models for both perspectives are presented as a means of bracketing discussion of the role of communication processes in group outcomes. The implications of these models for future theorizing are discussed. The first of these two models is an extension of Hewes's socioegocentric model (1986, 1996). The second class of formal model, dual-level connectionist models, integrates mental and communication processes to explain moment-by-moment communication behavior. This class of models is contrasted with important models of group influence that use atemporal aggregations of messages to predict group outcomes. Implications of dual-level connections models for the role of "emergence" in group theorizing, the limitations of Markovian models of group communication research, and the decomposability of psychological and communication processes are elaborated.