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The human brain exhibits recurrent oscillatory activity in cortical networks of neuronal populations, which are thought to play a role in specialized cognitive functions. However, it is not known whether these oscillatory network states evolve over time in a structured or random matter. In this study, we introduce a new method for analyzing the long-term evolution of these states, and demonstrate that they follow a cyclical architecture when the brain is at rest, with typical cycle durations of 300-500 milliseconds. This cyclical organization structure positions the default mode network (DMN) and dorsal attention network (DAN) at opposite phases of the cycle, with the DMN preceded by higher frequency oscillations in sensorimotor networks and followed by lower frequency oscillations in frontotemporal networks respectively. The cyclical structure was robust in three large magnetoencephalography (MEG) resting state datasets, and persists in a visuo-motor task, where cycle phase predicts reaction time. Moreover, individual cyclical dynamics were predictive of demographics: older people deviate less from the cycle structure and show a general slowing of cycle rate, and cycle rate is strongly heritable. These findings suggest that the evolution of oscillatory network states in the human brain may be more organized than previously thought and provide potential biomarkers for health and disease.