There is only one file type that uses the .NMC extension:
ArcGIS Explorer Map Content File
Packaged map content file created by ArcGIS Explorer, a free GIS application developed by ESRI; may contain various elements of a map, including notes, folders, views, links, image overlays, GIS service layers, KML layers, raster layers, feature layers, and layer packages; used for exporting map content and adding it to another map that is open in ArcGIS Explorer.
NMC files differ from .NMF files. While NMF files store a complete map that replaces the current map when opened, NMC files only add content to the currently-opened map. NMC files are useful for sharing map content with others. They can be emailed using the "E-Mail" option on the Tools tab. They may also be exported using the "Export" option on the Tools tab.
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Updated: November 23, 2010