Extraction of motion from visual input plays an important role in many visual tasks, such as separation of figure from ground and navigation through space. Several kinds of local motion signals have been distinguished based on mathematical and computational considerations (e.g., motion based on spatiotemporal correlation of luminance, and motion based on spatiotemporal correlation of flicker), but little is known about the prevalence of these different kinds of signals in the real world. To address this question, we first note that different kinds of local motion signals (e.g., Fourier, non-Fourier, and glider) are characterized by second- and higher-order correlations in slanted spatiotemporal regions. The prevalence of local motion signals in natural scenes can thus be estimated by measuring the extent to which each of these correlations are present in space-time patches and whether they are coherent across spatiotemporal scales. We apply this technique to several popular movies. The results show that all three kinds of local motion signals are present in natural movies. While the balance of the different kinds of motion signals varies from segment to segment during the course of each movie, the overall pattern of prevalence of the different kinds of motion and their subtypes, and the correlations between them, is strikingly similar across movies (but is absent from white noise movies). In sum, naturalistic movies contain a diversity of local motion signals that occur with a consistent prevalence and pattern of covariation, indicating a substantial regularity of their high-order spatiotemporal image statistics.