The coexistence of different Grid infrastructures and the advent of Grid services based on Web Services opens an interesting debate about the coordinated harnessing of resources based on different middleware implementations and even different Grid service technologies. In this paper, we present the loosely-coupled architecture of GridWay, which allows the coordinated use of different Grid infrastructures, although based on different Grid middlewares and services, as well as a straightforward resource sharing. This architecture eases the gradual migration from pre-WS Grid services to WS ones, and even, the long-term coexistence of both. We demonstrate its suitability with the evaluation of the coordinated use of two Grid infrastructures: a research testbed based on Globus WS Grid services, and a production testbed based on Globus pre-WS Grid services, as part of the LCG middleware.