When text symbolized with a dropshadow is exported to Adobe Illustrator format, the text is doubled in the output file. It appears as 'TextText' instead of 'Text'. On splined text, it will appear as 'TTeexxtt'.
The Adobe Illustrator format does not support the export of dropshadowed text.
Select a different symbol for the text. Dropshadows can be added in an external graphics application.
The Adobe Illustrator (.ai) export format is available for ArcMap at ArcGIS 8.1 Service Pack 1.