To address the issues of insufficient utilization of local details, the difficulty in balancing computational complexity and representation capability, and the inability of static templates to adapt to target appearance variations in Transformer-based visual object tracking, this paper proposes a multi-branch Agent Transformer tracking framework with spatiotemporal modeling, termed MBAST. Specifically, a multi-branch feature extraction network based on Agent Transformer is constructed, which preserves a global receptive field while reducing the computational complexity of attention from quadratic to approximately linear growth. A feature enhancement module is designed to strengthen the representation of target boundaries and local textures. Furthermore, a dynamic historical frame update mechanism is introduced to adaptively select representative frames, thereby improving long-term appearance modeling. In the feature fusion stage, bounding box geometric encoding is combined with an enhanced MLP to improve the robustness of target localization. Experimental results on GOT-10k and TrackingNet demonstrate that MBAST outperforms representative methods such as SwinTrack and TATrack across multiple metrics, and exhibits strong robustness and accuracy in challenging scenarios including background clutter, occlusion, and camera motion.