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Although continual learning and anomaly detection have separately been well-studied in previous works, their intersection remains rather unexplored. The present work addresses a learning scenario where a model has to incrementally learn a sequence of anomaly detection tasks, i.e. tasks from which only examples from the normal (majority) class are available for training. We define this novel learning problem of continual anomaly detection (CAD) and formulate it as a meta-learning problem. Moreover, we propose A Rapid Continual Anomaly Detector (ARCADe), an approach to train neural networks to be robust against the major challenges of this new learning problem, namely catastrophic forgetting and overfitting to the majority class. The results of our experiments on three datasets show that, in the CAD problem setting, ARCADe substantially outperforms baselines from the continual learning and anomaly detection literature. Finally, we provide deeper insights into the learning strategy yielded by the proposed meta-learning algorithm.