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This article explores federated long-tail learning (Fed-LT) tasks, which involve clients with private and heterogeneous data that exhibit a long-tail distribution. We propose two methods: (a) Client Re-weighted Prior Analyzer (CRePA), which balances the global model's performance on tail and non-tail categories and enhances performance on tail categories while maintaining it on non-tail categories. (b) Federated Long-Tail Causal Intervention Model (FedLT-CI) computes clients' causal effects on the global model's performance in the tail and enhances the interpretability of Fed-LT. CRePA achieves state-of-the-art performance, and FedLT-CI improves tail performance significantly without affecting non-tail performance. Extensive experiments indicate that CRePA achieved SOTA performance compared to other baselines on CIFAR-10-LT and CIFAR-100-LT. Applying the FedLT-CI to all baselines significantly improved tail performance without affecting non-tail performance.