Desktop grids, such as XtremWeb and BOINC, and service grids, such as EGEE, are two different approaches for science communities to gather computing power from a large number of computing resources. Nevertheless, little work has been done to combine these two Grid technologies in order to establish a seamless and vast grid resource pool. In this paper we present the EGEE service grid, the BOINC and XtremWeb desktop grids. Then, we present the EDGeS solution to bridge the EGEE service grid with the BOINC and XtremWeb desktop grids.