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A data model defines the types of structures present in a database and the types of operations which may be used to alter the database. An understanding of data model equivalence properties is necessary if one wishes to implement a system which presents different uses with views of a database in terms of differing data models or which provides a common interface to several database systems defined in terms of different data models. Requisites for this understanding are formal definitions of the involved concepts and a formal framework in which different data models can be compared. This thesis presents formal definitions of the terms database, operation, operation type, application model. Database state equivalence, operation equivalence, application model equivalence and data model equivalence are distinguished. Three types of application and data model equivalence are defined - isomorphic, composed operation and state dependent. Implementation implications of these different equivalences are discussed. It is proved that the semantic graph and the restricted semantic relation data models are state dependent equivalent. Observations on the network vs. relational data model 'controversy' are presented. SUggestions for applications of this research include a dual semantic data model interface.