Abstract: Hunting instability represents a critical dynamic issue that significantly hinders both the running stability and operational safety of high-speed trains. The occurrence of severe hunting motion triggers intense wheel-rail interactions, thereby posing a grave threat to safe train operations. Within the current research landscape, the majority of existing studies rely primarily on bogie frame acceleration signals to determine the presence of hunting instability. However, these conventional methods generally classify the motion into only two basic categories: the hunting state and the normal state. Because they lack the detailed characterization of dynamic features throughout the entire instability evolution process, these methods exhibit insufficient accuracy when identifying the precise stability states of hunting motion. Consequently, achieving a fine-grained classification of hunting stability remains a highly challenging task. To effectively address this critical issue, this paper proposes a graded identification method for assessing hunting motion. This approach is fundamentally based on the axle-box acceleration phase difference between the longitudinal and lateral accelerations, as well as their respective harmonic characteristics, thereby tackling the problem directly from the perspective of wheel-rail contact geometric nonlinearity. Firstly, based on the independent wheelset model, a thorough analysis and subsequent validation are conducted on the phase synchronization characteristics of the lateral and longitudinal accelerations, which embody the underlying kinematic mechanisms, and on the harmonic characteristics of the lateral acceleration, which reflect the contact nonlinearity. The proposed method employs these phase coupling characteristics to establish a phase locking index. This crucial step realizes the qualitative identification of hunting motion, effectively distinguishing the unstable hunting state from the normal operation state. Building upon this theoretical foundation, the harmonic characteristics are then utilized to from a total harmonic distortion index intended to determine the exact hunting severity. Through this systematic approach, the method achieves a fine-grained, graded identification regarding the severity of hunting motion experienced by high-speed trains. Simulation results for verification demonstrate that the proposed method is fully capable of performing an accurate grading evaluation of hunting severity under a wide variety of complex operating conditions. Compared with the current industry standards, this novel method realizes a significant transition from mere "qualitative discrimination" to a comprehensive "severity graded identification" of hunting motion for high-speed trains. Consequently, it provides highly valuable technical support for the quantitative assessment of hunting stability.