I just created this video after a bit of trial and error (and research!) that demonstrates how to set up:

CamStudio 2.6 Beta (official download link)

so that the audio and video stay in synchronization throughout the length of the video. (Or download the Most Stable Camstudio 2.0 release) Getting CamStudio to synchronize the video to the audio requires that the “Playback Rate” in Video Options divides evenly into 1000 milliseconds, with the result being placed in the entry that goes in the box above it, “Capture Frames Every”. This must be a whole number (no fractions). This basically means that you have five options for playback rate/frames per second (as CamStudio does not allow fractional entries in the “Capture Frames Every” box). You must use, therefore, 40 milliseconds with 25 frames/sec, or 50 milliseconds with 20 frames/sec, or 100 milliseconds with 10 frames per second, or, if you are a mad scientist, 20 milliseconds with 50 frames/sec or 25 milliseconds with 40 frames/sec. The first two settings mentioned are plenty adequate for 90% of applications, though. Any other settings will cause a lag to develop in the audio that will get worse and worse as time passes.