The Testbed and Applications working group of the European Grid Forum (EGrid) is actively building and experimenting with a grid infrastructure connecting several research-based supercomputing sites located in Europe. This paper reports on our first feasibility study: running a self-migrating version of the Cactus simulation code across the European grid testbed, including "live" remote data visualization and steering from different demonstration booths at Supercomputing 2000, in Dallas, TX. We report on the problems that had to be resolved for this endeavour and identify open research challenges for building productiongrade grid environments.