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Temporal variability is a fundamental property of brain processes and is functionally important to human cognition. This study examined how fluctuations in neural oscillatory activity are related to problem-solving performance as one example of how temporal variability affects high-level cognition. We used volatility to assess step-by-step fluctuations of EEG spectral power while individuals attempted to solve word-association puzzles. Inspired by recent results with hidden-state modeling, we tested the hypothesis that spectral-power volatility is directly associated with problem-solving outcomes. As predicted, volatility was lower during trials solved with insight compared with those solved analytically. Moreover, volatility during prestimulus preparation for problem-solving predicted solving outcomes, including solving success and solving time. These novel findings were replicated in a separate data set from an anagram-solving task, suggesting that less-rapid transitions between neural oscillatory synchronization and desynchronization predict better solving performance and are conducive to solving with insight for these types of problems. Thus, volatility can be a valuable index of cognition-related brain dynamics. [ABSTRACT FROM AUTHOR]