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Animal behavior can be decomposed into a sequence of discrete activity bouts over time. Analyzing the statistical structure of such behavioral sequences can provide insights into the drivers of behavioral decisions. Laboratory studies, predominantly in invertebrates, have suggested that behavioral sequences exhibit multiple timescales and long-range memory, but whether these results can be generalized to other taxa and to animals in natural settings remains unclear. By analyzing accelerometer-inferred predictions of behavioral states in three species of social mammals (meerkats, white-nosed coatis, and spotted hyenas) in the wild, we found surprisingly consistent structuring of behavioral sequences across all behavioral states, all individuals, and all study species. Behavioral bouts were characterized by decreasing hazard functions, wherein the longer a behavioral bout had progressed, the less likely it was to end within the next instant. The predictability of an animal’s future behavioral state as a function of its present state always decreased as a truncated power-law for predictions made farther into the future, with very similar estimates for the power law exponent across all species. Finally, the distributions of bout durations were also heavy-tailed. Why such shared structural principles emerge remains unknown, and we explore multiple plausible explanations, including environmental nonstationarity, behavioral self-reinforcement, and the hierarchical nature of behavior. The existence of highly consistent patterns in behavioral sequences across our study species suggests that these phenomena could be widespread in nature, and points to the existence of fundamental properties of behavioral dynamics that could drive such convergent patterns.