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The impressive variety of biological rhythms leaves no doubt that autonomously periodic processes contribute to the coordination of life-processes. The question here raised is, “What modes of temporal organization—if any—could result from weak interactions in a population of innately oscillatory devices (e.g. electronic oscillators, secretory cells, spontaneously active neurons, or individual animals)?” By mathematical analysis, electronic experiments, and digital computer simulation, answers are found as functions of the nature of the periodic processes and the kind of interactions involved. For populations of “generalized relaxation oscillators”, threshold conditions are discovered for mutual synchronization in any of a variety of modes. It is proposed that self-entraining communities of this sort may exist within individual metazoan animals and plants as the basis of the observed diurnal coordination of their physiological process.