I want to explore it in ArcMap or in ArcExplorer but both cannot "see" it. For the other resources like map services everything is workikng well. I can add that the service is started and in a preview view eveything seems to be ok.
ArcMap and ArcExplorer (not to be confused with ArcGIS Explorer) are 2D clients and cannot consume a globe service. You'll need to use a 3D client like ArcGlobe or ArcGIS Explorer to use your globe service.