Don; moving how? You mean away from the fence?
Possible contributors:
-wrong blade...too fine/too many teeth (see the thread on sawblades)
- fence not parallel to the blade (plus a couple of thou extra at the outfeed end)
-no riving knife or splitter in place?
-no featherboards on the infeed side of the blade (holding the stock against the fence)
-the material has built in tension, and it's released during the cut
-the fence moves?
-blade needs cleaning/sharpening?
Not suggesting that you haven't considered all of the above, Don, but those are just a list of the most common factors. Guessing that the list will be added to/corrected shortly.

If it were me, I'd be taking a long hard look at my blade; this kind of sneaks up on you over time. I'd be using my circ saw for months, then I'd get frustrated because it seemed that the saw would start pulling to the right on a rip cut. I'd put on a new blade and like magic the problem would go away and the saw would cut like a hot knife through butter. *embarrassment*