Harnessing low-light enhancement and domain adaptation, nighttime UAV tracking has made substantial strides. However, over-reliance on image enhancement, scarcity of high-quality nighttime data, and neglecting the relationship between daytime and nighttime trackers, which hinders the development of an end-to-end trainable framework. Moreover, current CNN-based trackers have limited receptive fields, leading to suboptimal performance, while ViT-based trackers demand heavy computational resources due to their reliance on the self-attention mechanism. In this paper, we propose a novel pure Mamba-based tracking framework (\textbf{MambaNUT}) that employs a state space model with linear complexity as its backbone, incorporating a single-stream architecture that integrates feature learning and template-search coupling within Vision Mamba. We introduce an adaptive curriculum learning (ACL) approach that dynamically adjusts sampling strategies and loss weights, thereby improving the model's ability of generalization. Our ACL is composed of two levels of curriculum schedulers: (1) sampling scheduler that transforms the data distribution from imbalanced to balanced, as well as from easier (daytime) to harder (nighttime) samples; (2) loss scheduler that dynamically assigns weights based on data frequency and the IOU. Exhaustive experiments on multiple nighttime UAV tracking benchmarks demonstrate that the proposed MambaNUT achieves state-of-the-art performance while requiring lower computational costs. The code will be available.