All-in-one models for adverse weather removal aim to process various degraded images using a single set of parameters, making them ideal for real-world scenarios. However, they encounter two main challenges: catastrophic forgetting and limited degradation awareness. The former causes the model to lose knowledge of previously learned scenarios, reducing its overall effectiveness. While the later hampers the model’s ability to accurately identify and respond to specific types of degradation, limiting its performance across diverse adverse weather conditions. To address these issues, we introduce the Incremental Learning Adverse Weather Removal (ILAWR) framework, which uses a novel degradation-aware distillation strategy for continuous weather removal. Specifically, we first design a degradation-aware module that utilizes Fourier priors to capture a broad range of degradation features, effectively mitigating catastrophic forgetting in low-level visual tasks. Then, we implement multilateral distillation, which combines knowledge from multiple teacher models using an importance-guided aggregation approach. This enables the model to balance adaptation to new degradation types with the preservation of background details. Extensive experiments on both synthetic and real-world datasets confirm that ILAWR outperforms existing models across multiple benchmarks, proving its effectiveness in continuous adverse weather removal.