The lines you see are noise at a 60Hz repetition rate (AC line
frequency) getting into the video. The lack of phase lock between
the computer's video refresh rate (60Hz) and the AC mains causes
the lines to drift at constant speed relative to the computer-
synchronized raster.
You mentioned that you just noticed them. Have they recently
appeared, or is it possible they've been there for some time?
I ask, because if you have recently changed the position of the
monitor or some electrical device around it, that change may
be responsible for the problem. If so, try changing things back
to see if you can isolate the problem.