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Federated Learning (FL) enables training state-of-the-art Automatic Speech Recognition (ASR) models on user devices (clients) in distributed systems, hence preventing transmission of raw user data to a central server. A key challenge facing practical adoption of FL for ASR is obtaining ground-truth labels on the clients. Existing approaches rely on clients to manually transcribe their speech, which is impractical for obtaining large training corpora. A promising alternative is using semi-/self-supervised learning approaches to leverage unlabelled user data. To this end, we propose FedNST, a novel method for training distributed ASR models using private and unlabelled user data. We explore various facets of FedNST, such as training models with different proportions of labelled and unlabelled data, and evaluate the proposed approach on 1173 simulated clients. Evaluating FedNST on LibriSpeech, where 960 hours of speech data is split equally into server (labelled) and client (unlabelled) data, showed a 22.5% relative word error rate reduction} (WERR) over a supervised baseline trained only on server data.