When humans talk without conventionalized arrangements, they engage in conversation--that is, a continuous and largely nonsimultaneous exchange in which speakers take turns. Turn-taking is ubiquitous in conversation and is the normal case against which alternatives, such as interruptions, are treated as violations that warrant repair. Furthermore, turn-taking involves highly coordinated timing, including a cyclic rise and fall in the probability of initiating speech during brief silences, and involves the notable rarity, especially in two-party conversations, of two speakers' breaking a silence at once. These phenomena, reported by conversation analysts, have been neglected by cognitive psychologists, and to date there has been no adequate cognitive explanation. Here, we propose that, during conversation, endogenous oscillators in the brains of the speaker and the listeners become mutually entrained, on the basis of the speaker's rate of syllable production. This entrained cyclic pattern governs the potential for initiating speech at any given instant for the speaker and also for the listeners (as potential next speakers). Furthermore, the readiness functions of the listeners are counterphased with that of the speaker, minimizing the likelihood of simultaneous starts by a listener and the previous speaker. This mutual entrainment continues for a brief period when the speech stream ceases, accounting for the cyclic property of silences. This model not only captures the timing phenomena observed inthe literature on conversation analysis, but also converges with findings from the literatures on phoneme timing, syllable organization, and interpersonal coordination.