Nonperiodic cycles occur in times series obtained in many chemical engineering applications. Variations in the cycle characteristics provide valuable information about the system in which the time series was measured. New methods are developed to detect cycles and determine their characteristics such as the cycle time, its regularity, the cycle strength, and the regularity of the cycle amplitude. These methods are thoroughly validated with both mathematically generated and experimental time series. The best detection method for nonperiodic cycles uses either the V statistic or, if it fails, the new, more sensitive, but more complex, P statistic. Cycle characteristics can be used to detect flow regime transitions in multiphase systems such as risers, gas-solid, and gas-liquid-solid fluidized beds using signals from a variety of simple probes.