Oil Spill Detection (OSD) in remote sensing images is commonly viewed as a semantic segmentation task.However, due to the the small proportion of oil spill area within images, existing OSD datasets tend to be class imbalance, posing significant challenges for convolutional neural network (CNN)-based segmentation models because their limited receptive fields.In this study, we introduce OSDMamba, which is the first Mamba-based architecture specifically designed for oil spill detection.Comparing to CNN, OSDMamba leverages Mamba' selective scanning mechanism to effectively expand the model’s receptive field while preserving critical details.To further enhance performance, we propose an asymmetric decoder that integrates state-space modeling and deep supervision, improving multi-scale feature fusion and increasing sensitivity to minority-class samples.In our experiments, the proposed OSDMamba achieves state-of-the-art performance, outperforming CNN-based models with improvements of 8.9\% and 11.8\% in terms of mIoU across two OSD datasets, demonstrating its effectiveness.