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We propose a new dynamic model which can be used within blob trackers to track the target's center of gravity. A strong point of the model is that it is designed to track a variety of motions which are usually encountered in applications such as pedestrian tracking, hand tracking, and sports. We call the dynamic model a two-stage dynamic model due to its particular structure, which is a composition of two models: a liberal model and a conservative model. The liberal model allows larger perturbations in the target's dynamics and is able to account for motions in between the random-walk dynamics and the nearly constant-velocity dynamics. On the other hand, the conservative model assumes smaller perturbations and is used to further constrain the liberal model to the target's current dynamics. We implement the two-stage dynamic model in a two-stage probabilistic tracker based on the particle filter and apply it to two separate examples of blob tracking: 1) tracking entire persons and 2) tracking of a person's hands. Experiments show that, in comparison to the widely used models, the proposed two-stage dynamic model allows tracking with smaller number of particles in the particle filter (e.g., 25 particles), while achieving smaller errors in the state estimation and a smaller failure rate. The results suggest that the improved performance comes from the model's ability to actively adapt to the target's motion during tracking.