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Multidimensional semistructured data (MSSD) are semistructured data that present different facets under different contexts. Context represents alternative worlds, and is expressed by assigning values to a set of user-defined variables called dimensions. The notion of context has been incorporated in the object exchange model (OEM), and the extended model is called Multidimensional OEM (MOEM), a graph model for MSSD. In this paper, we explain in detail how MOEM can represent the history of an OEM database. We discuss how MOEM properties are applied in the case of representing OEM histories, and show that temporal OEM snapshots can be obtained from MOEM. We present a system that implements the proposed ideas, and we use an example scenario to demonstrate how an underlying MOEM database accommodates changes in an OEM database. Furthermore, we show that MOEM is capable to model changes occurring not only in OEM databases, but in Multidimensional OEM databases as well. The use of multidimensional query language (MQL), a query language for MSSD, is proposed for querying the history of OEM databases and MOEM databases.