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We address the development of a normalization theory for object-oriented data models that have common features to support objects. We first provide an extension of functional dependencies to cope with the richer semantics of relationships between objects, called path dependency, local dependency, and global dependency constraints. Using these dependency constraints, we provide normal forms for object-oriented data models based on the notions of user interpretation (user-specified dependency constraints) and object model. In constrast to conventional data models in which a normalized object has a unique interpretation, in object-oriented data models, an object may have many multiple interpretations that form the model for that object. An object will then be in a normal form if and only if the user's interpretation is derivable from the model of the object. Our normalization process is by nature iiterative, in which objects are restructured until their models reflect the user's interpretation.