"Stereo Mix" can also be "Wave", "Wave Out Mix",
"What U Hear" or similarly labelled sources (the actual name depends highly on the sound card and driver). If none of these are listed, start recording, then try selecting each source until you find the one that works.
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However, some sound cards do not have any way of internally recording the audio directly while it is also internally playing something (aka "duplex"). But in that case, chances are that your sound card is capable of outputting something externally (speakers) while it can record from an external source (mic, line-in).
If this is the case, you will need to buy or make a short stereo splitter cable to connect the sound card's output (green) to its Line-in (blue), then select "Line" as the source.
easy temporarly solution (you need to disconnect the speakers, thus you wont physically hear a thing)
or
permanent solution, no need to disconnect the speakers each time
Only very old cards are also not capable of doing this; they can only do 1 thing at the time.
(and I mean old as in almost extinct)
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Previous threads with exact the same question (and very detailed info):
Recording Sound??
CookieRevised's reply to Make programs think that...
MSN audio coversation