Despite various interoperability recommendations, heterogeneity of Geographic Information Systems (GIS) is still an issue. This led to an increasing need for a data integration system that allows transparent and uniform access to spatial data disseminated over a network. In this paper, we describe the internals of query processing in the VirGIS mediation system. Recall that a data mediation system provides users with a uniform access to a multitude of (local/remote) data sources, without duplicating the data. The user poses his query against a virtual (global) schema, the query is in turn rewritten into queries sent to the local sources. VirGIS complies with Open GIS Consortium recommendations in using the Geography Markup Language (GML) for the encoding and the transport of geographic information, and the Web Feature Server (WFS) interfaces to perform communications with clients and data sources. Categories and Subject Descriptors H.2.8 [DATABASE MANAGEMENT]: Database Applications --...