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Characterization of large-scale brain networks using blood-oxygenation-level-dependent functional magnetic resonance imaging is typically based on the assumption of network stationarity across the duration of scan. Recent studies in humans have questioned this assumption by showing that within-network functional connectivity fluctuates on the order of seconds to minutes. Time-varying profiles of resting-state networks (RSNs) may relate to spontaneously shifting, electrophysiological network states and are thus mechanistically of particular importance. However, because these studies acquired data from awake subjects, the fluctuating connectivity could reflect various forms of conscious brain processing such as passive mind wandering, active monitoring, memory formation, or changes in attention and arousal during image acquisition. Here, we characterize RSN dynamics of anesthetized macaques that control for these accounts, and compare them to awake human subjects. We find that functional connectivity among nodes comprising the "oculomotor (OCM) network" strongly fluctuated over time during awake as well as anaesthetized states. For time dependent analysis with short windows (<60 s), periods of positive functional correlations alternated with prominent anticorrelations that were missed when assessed with longer time windows. Similarly, the analysis identified network nodes that transiently link to the OCM network and did not emerge in average RSN analysis. Furthermore, time-dependent analysis reliably revealed transient states of large-scale synchronization that spanned all seeds. The results illustrate that resting-state functional connectivity is not static and that RSNs can exhibit nonstationary, spontaneous relationships irrespective of conscious, cognitive processing. The findings imply that mechanistically important network information can be missed when using average functional connectivity as the single network measure.