Chapple's model of dyadic face-to-face social interaction describes how conversation partners develop mutually entrained activity cycles over time. Past applications of frequency domain analysis to noncontent vocal activity in adult conversations document that vocal activity and other behavioral and physiological processes do tend to vary cyclically during social interaction, as Chapple's theory predicts. However, the observed cycles in amount of talk are irregular, and it has been suggested that they represent only a stochastic variation rather than the operation of deterministic mechanisms. The present study demonstrates that cyclicity in amount of talk increases over time as a conversation progresses, possibly because of mutual entrainment between partner activity rhythms. Periodogram analysis of 83 conversations in opposite sex adult stranger dyads indicated that the average percent of variance due to cyclicity increased from 37% in the first ten minutes to 42% in the last ten minutes of forty-minute get-acquainted conversations; this increase was statistically significant, p < .05. No gender differences in cyclicity were found. Results were interpreted as support for Chapple's nonlinear systems model of social interaction, which describes dyadic social interaction as a loosely coupled ensemble of physiological and behavioral rhythms.KEY WORDS: individual, dyad, social interaction system, time and frequency domain TYPE OF ARTICLE: application of mathematical model DMSIONS AND UNITS: amount of talk per 10 second time units HAPPLE (1970) PROPOSED a nonlinear C systems theory t o describe variations in speaker activity over time during face-to-face dyadic social interaction. In his model, an individual speaker tends t o show a periodic alternation between periods of activity and inaction; this alternation between more and less activity is related t o internal physiological rhythms. When two people interact, they t r y to coordinate their vocal activity to achieve