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As the network slicing is one of the critical enablers in communication networks, one anomalous physical node (PN) or physical link (PL) in substrate networks that carries multiple virtual network elements can cause significant performance degradation of multiple network slices. To recover the substrate networks from anomaly within a short time, rapid and accurate identification of whether or not the anomaly exists in PNs and PLs is vital. Online anomaly detection methods that can analyze system data in real-time are preferred. Besides, as virtual nodes and links mapped to PNs and PLs are scattered in multiple slices, the distributed detection modes are required to adapt to the virtualized environment. According to those requirements, in this paper, we first propose a distributed online PN anomaly detection algorithm based on a decentralized one-class support vector machine (OCSVM), which is realized through analyzing real-time measurements of virtual nodes mapped to PNs in a distributed manner. Specifically, to decouple the OCSVM objective function, we transform the original problem to a group of decentralized quadratic programming problems by introducing the consensus constraints. The alternating direction method of multipliers is adopted to achieve the solution for the distributed online PN anomaly detection. Next, by utilizing the correlation of measurements between neighbor virtual nodes, another distributed online PL anomaly detection algorithm based on the canonical correlation analysis is proposed. The network only needs to store covariance matrices and mean vectors of current data to calculate the canonical correlation vectors for real-time PL anomaly analysis. The simulation results on both synthetic and real-world network datasets show the effectiveness and robustness of the proposed distributed online anomaly detection algorithms.