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The paper focuses on and takes the shape of an approach meant to mediate the interaction between the Geospatial and the Grid infrastructures by introducing a new component referred to as Mediator. The component shall diminish the gap between the two infrastructures and create an interoperable communication. The solution thereinafter advanced aims at adapting the Geospatial services so as to follow different execution flows, either on the Web or on the Grid, by considering the input conditions and the running platforms as factors required to maximize the execution performances.