<p>Temporal motion modeling has always been a key component in multiple object tracking (MOT), which can ensure smooth trajectories and provide accurate positional information to enhance association precision. However, current motion models struggle to be both efficient and effective across different application scenarios. To this end, we propose TrackSSM, inspired by the recently popular state space models (SSMs), a unified encoder-decoder motion framework that uses a data-dependent state space model to perform temporal motion prediction of trajectories. Specifically, we propose Flow-SSM, a module that utilizes the position and motion information from historical trajectories to guide the temporal state transition of object bounding boxes. Based on Flow-SSM, we design a flow decoder. It is composed of a cascaded motion decoding module employing Flow-SSM, which can use the encoded flow information to complete the temporal position prediction of trajectories. Additionally, we propose a step-by-step linear (S²L) training strategy. By performing linear interpolation between the positions of the object in the previous frame and the current frame, we construct the pseudo labels of step-by-step linear training, ensuring that the trajectory flow information can better guide the object bounding box in completing temporal transitions. TrackSSM utilizes a simple Mamba-Block to build a motion encoder for historical trajectories, forming a temporal motion model with an encoder-decoder structure in conjunction with the flow decoder. TrackSSM is applicable to various tracking scenarios and achieves excellent tracking performance across multiple benchmarks, further extending the potential of SSM-like temporal motion models in multi-object tracking tasks. Code and models are publicly available at <a href="https://github.com/Xavier-Lin/TrackSSM">https://github.com/Xavier-Lin/TrackSSM</a>.</p>