This paper introduces the concept of eigen-dynamics and proposes an eigen dynamics analysis (EDA) method to learn the dynamics of natural hand motion from labelled sets of motion captured with a data glove. The result is parameterized with a high-order stochastic linear dynamic system (LDS) consisting of five lower-order LDS. Each corresponding to one eigen-dynamics. Based on the EDA model, we construct a dynamic Bayesian network (DBN) to analyze the generative process of a image sequence of natural hand motion. Using the DBN, a hand tracking system is implemented. Experiments on both synthesized and real-world data demonstrate the robustness and effectiveness of these techniques.