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Federated learning (FL) is known to be susceptible to model poisoning attacks in which malicious clients hamper the accuracy of the global model by sending manipulated model updates to the central server during the FL training process. Existing defenses mainly focus on Byzantine-robust FL aggregations, and largely ignore the impact of the underlying deep neural network (DNN) that is used to FL training. Inspired by recent findings on critical learning periods (CLP) in DNNs, where small gradient errors have irrecoverable impact on the final model accuracy, we propose a new defense, called a CLP-aware defense against poisoning of FL (DeFL). The key idea of DeFL is to measure fine-grained differences between DNN model updates via an easy-to-compute federated gradient norm vector (FGNV) metric. Using FGNV, DeFL simultaneously detects malicious clients and identifies CLP, which in turn is leveraged to guide the adaptive removal of detected malicious clients from aggregation. As a result, DeFL not only mitigates model poisoning attacks on the global model but also is robust to detection errors. Our extensive experiments on three benchmark datasets demonstrate that DeFL produces significant performance gain over conventional defenses against state-of-the-art model poisoning attacks.