Abstract.The axis‐crossing counts in a time series and in its successive differences are called higher‐order crossings (HOC). Under the Gaussian assumption the sequence of expected HOC is monotone increasing and admits a spectral representation which establishes a clear connection between HOC and the spectrum. In particular the normalized number of axis‐crossings (first HOC) tends to admit values at or near a dominant frequency, while the sequence of normalized HOC converges to the highest frequency in the spectrum. When the series is first lowpass filtered, the resulting normalized HOC tend to ‘visit’ true discrete frequencies on their way to the highest frequency. If the successive differences are replaced by successive summation, the resulting modified normalized HOC converge monotonically to the lowest frequency in the