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Federated learning (FL) has attracted growing attention via data-private collaborative training on decentralized clients. However, most existing methods unrealistically assume object classes of the overall framework are fixed over time. It makes the global model suffer from significant catastrophic forgetting on old classes in real-world scenarios, where local clients often collect new classes continuously and have very limited storage memory to store old classes. Moreover, new clients with unseen new classes may participate in the FL training, further aggravating the catastrophic forgetting of the global model. To address these challenges, we develop a novel Global-Local Forgetting Compensation (GLFC) model, to learn a global class incremental model for alleviating the catastrophic forgetting from both local and global perspectives. Specifically, to address local forgetting caused by class imbalance at the local clients, we design a class-aware gradient compensation loss and a class-semantic relation distillation loss to balance the forgetting of old classes and distill consistent inter-class relations across tasks. To tackle the global forgetting brought by the non-i.i.d class imbalance across clients, we propose a proxy server that selects the best old global model to assist the local relation distillation. Moreover, a prototype gradient-based communication mechanism is developed to protect privacy. Our model outperforms state-of-the-art methods by 4.4%-15.1% in terms of average accuracy on representative benchmark datasets.