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Multiple object tracking (MOT) from unmanned aerial vehicle (UAV) platforms requires efficient motion modeling. This is because UAV-MOT faces both local object motion and global camera motion. Motion blur also increases the difficulty of detecting large moving objects. Previous UAV motion modeling approaches either focus only on local motion or ignore motion blurring effects, thus limiting their tracking performance and speed. To address these issues, we propose the Motion Mamba Module, which explores both local and global motion features through cross-correlation and bi-directional Mamba Modules for better motion modeling. To address the detection difficulties caused by motion blur, we also design motion margin loss to effectively improve the detection accuracy of motion blurred objects. Based on the Motion Mamba module and motion margin loss, our proposed MM-Tracker surpasses the state-of-the-art in two widely open-source UAV-MOT datasets. Code will be available.