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The current effort to extend the power of information systems by making use of the semantics associated with terms and structures has resulted in a need to establish correspondences between different systems to allow a rich exchange of information. This paper describes the early efforts taking place in the STASIS project to identify the issues underlying support for mapping of corresponding entities between such heterogeneous systems. The STASIS system is meant to help a user establish such mappings by exploiting a semantic environment where he/she can contribute his/her own entities and relate them with other pre-existing entities. This process needs support at the entity representation level, to encapsulate each item into an appropriately rich representation structure, and at the logical level, where the resulting model is verified for consistency towards its future use. Examples are offered and discussed to highlight the issues and propose solutions.