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Federated semi-supervised learning (FSSL), facilitates labeled clients and unlabeled clients jointly training a global model without sharing private data. Existing FSSL methods predominantly employ pseudo-labeling and consistency regularization to exploit the knowledge of unlabeled data, achieving notable success in raw data utilization. However, these training processes are hindered by large deviations between uploaded local models of labeled and unlabeled clients, as well as confirmation bias introduced by noisy pseudo-labels, both of which negatively affect the global model's performance. In this paper, we present a novel FSSL method called Dual Class-aware Contrastive Federated Semi-Supervised Learning (DCCFSSL). This method accounts for both the local class-aware distribution of each client's data and the global class-aware distribution of all clients' data within the feature space. By implementing a dual class-aware contrastive module, DCCFSSL establishes a unified training objective for different clients to tackle large deviations and incorporates contrastive information in the feature space to mitigate confirmation bias. Moreover, DCCFSSL introduces an authentication-reweighted aggregation technique to improve the server's aggregation robustness. Our comprehensive experiments show that DCCFSSL outperforms current state-of-the-art methods on three benchmark datasets and surpasses the FedAvg with relabeled unlabeled clients on CIFAR-10, CIFAR-100, and STL-10 datasets. To our knowledge, we are the first to present an FSSL method that utilizes only 10\% labeled clients, while still achieving superior performance compared to standard federated supervised learning, which uses all clients with labeled data.