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Purpose: Bronchoscopic intervention is a widely-used clinical technique for pulmonary diseases, which requires an accurate and topological complete airway map for its localization and guidance. The airway map could be extracted from chest computed tomography (CT) scans automatically by airway segmentation methods. Due to the complex tree-like structure of the airway, preserving its topology completeness while maintaining the segmentation accuracy is a challenging task. Methods: In this paper, a long-term slice propagation (LTSP) method is proposed for accurate airway segmentation from pathological CT scans. We also design a two-stage end-to-end segmentation framework utilizing the LTSP method in the decoding process. Stage 1 is used to generate a coarse feature map by an encoder-decoder architecture. Stage 2 is to adopt the proposed LTSP method for exploiting the continuity information and enhancing the weak airway features in the coarse feature map. The final segmentation result is predicted from the refined feature map. Results: Extensive experiments were conducted to evaluate the performance of the proposed method on 70 clinical CT scans. The results demonstrate the considerable improvements of the proposed method compared to some state-of-the-art methods as most breakages are eliminated and more tiny bronchi are detected. The ablation studies further confirm the effectiveness of the constituents of the proposed method. Conclusion: Slice continuity information is beneficial to accurate airway segmentation. Furthermore, by propagating the long-term slice feature, the airway topology connectivity is preserved with overall segmentation accuracy maintained.