Both the federated approach and the mediator approach to database integration require that semantic diierences between schemas be resolved by a process of schema transformation. Data, queries and updates subsequently passed between schemas need to be transformed accordingly. We have developed a general framework to support the schema transformation process. This framework consists of a graph-based common data model and a set of primitive schema transformations deened for this model. Higher-level common data models and primitive schema transformations for them can be deened in terms of this lower-level model. Primitive transformations can be composed into composite ones. This paper gives an overview of our framework and then shows how to deene an Entity-Relationship common data model and schema transformations on it. The key feature of our framework is that both primitive and composite schema transformations are automatically reversible. We show how these transformations can be used to automatically migrate or wrap data, queries and updates between semantically equivalent schemas. We describe a prototype schema integration tool that supports this functionality. We also show how to handle transformations between non-equivalent but overlapping schemas. Finally, we discuss how our approach can be extended to more sophisticated application logic such as constraints, deductive rules, and active rules. The contribution of the paper is that we provide a general solution to the problem of moving data and queries between schemas in federated and mediated multi-database archi-tectures.