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An .asx file is a text file, containing a link to an .asf, Microsoft's Active Streaming Format. Play using VLC or Flip4Mac.
 
I know .asf definitely is. I hadn't heard of .asx, but I did a google search (.asx mac) which wasn't that helpful other than some mention of windows media player. You should try downloading Flip4Mac which is a plugin for quicktime making it like WMP.

EDIT: Beaten to it...
 
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