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Recently, unsupervised person re-identification (Re-ID) has received increasing research attention due to its potential for label-free applications. A promising way to address unsupervised Re-ID is clustering-based, which generates pseudo labels by clustering and uses the pseudo labels to train a Re-ID model iteratively. However, most clustering-based methods take each cluster as a pseudo identity class, neglecting the intra-cluster variance mainly caused by the change of cameras. To address this issue, we propose to split each single cluster into multiple proxies according to camera views. The camera-aware proxies explicitly capture local structures within clusters, by which the intra-ID variance and inter-ID similarity can be better tackled. Assisted with the camera-aware proxies, we design two proxy-level contrastive learning losses that are, respectively, based on offline and online association results. The offline association directly associates proxies according to the clustering and splitting results, while the online strategy dynamically associates proxies in terms of up-to-date features to reduce the noise caused by the delayed update of pseudo labels. The combination of two losses enables us to train a desirable Re-ID model. Extensive experiments on three person Re-ID datasets and one vehicle Re-ID dataset show that our proposed approach demonstrates competitive performance with state-of-the-art methods. Code will be available at: https://github.com/Terminator8758/O2CAP.