In data-integration systems, the queries supported by a mediator are affected by the query-processing limitations of the sources being integrated. Existing mediation systems employ a variety of mechanisms to describe the query-processing capabilities of sources. However, these systems do not compute the capabilities of the mediators based on those of the sources they integrate. In this paper, we propose a framework to capture a rich variety of query-processing capabilities, and present algorithms to compute the set of mediator supported queries based on the capability limitations of its sources. Our algorithms take into consideration a variety of query-processing techniques employed by mediators to enhance the set of supported queries, and they yield concise capability descriptions. By computing mediator query capabilities, and representing them in the same way as those of data sources, we enable mediators to be used by other mediators, and we also make it easier for end users to know in advance which mediator queries are feasible. Keywords: Data Integration, Heterogeneous Databases, Mediators.