Hi,
The answer depends on what you meant by "store basemaps locally".
I'm guessing that you'd like to use ArcGIS Explorer in a disconnected environment but you'd still like access to the ESRI basemap data? The answer to this scenario is no you can't. Basemaps are simple XML files that reference data sources and in the case of the ESRI supplied basemaps all the sources are to services (ArcGIS Server, Bing Maps etc.). As you navigate the map, the data is cached onto your PC - for the ArcGIS Server data it gets cached permantently, for Bing it is cached for the lifetime the app is running. Here's the key point - ArcGIS Explorer must be connected to the internet when it starts in order to use any of the ESRI basemaps (even if the data is already cached) as it is designed to work in an internet-connected environment. If on the other hand, you disconnect from the internet while explorer is running you should be able to see any data that had already been cached.
If you want to make a basemap from your local data (on your pc) - then this is possible. From the Pearl select Save As then New Basemap
Mike Rudden
ESRI
