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I can't simultaneously left and right click. It is only possible to activate both mouse buttons sequentially thus it is not possible to use spells which require the activation of both left and right mouse click at the same time. Anyone else encountered this problem and is there anything that can be done about this?

I vaugley remember a problem like this, but I can't remember how it was fixed.  How did you install Skyrim?

You could try installing some packages like:

• xinput
• dinput

Or some other Direct X packages.  It may be trial-n-error to figure this out