Could be that your wheels are out of balance or out of round. That is pretty common on dirt bikes, but since most people don't take them to high speeds of 60+ mph on hard pack roads, they just don't notice. It could also be that one side of the rear axle is further back than the other - take a tape measure and check distance to the center of the axle on each side from the swingarm pivot.
There are a lot of other things that could contrbute to your problem, such as bad swing arm bearings, wheel bearings, or steering head bearings. If the bike is newer and in good shape, you can rule some of these things out.
You'll know hadshake when you get it. That's when your handle bars start slapping back and forth and the bike starts wobbling all over the place. The next thing that happens is - you are lucky enough to pull out of it or you wipe out really good.
My KDX is a great trail bike that turns on a dime but the short wheelbase makes it squirlly at high speeds. Your may want to try raising the forks as high as they will go in the clamps or do what I am thinking of doing......WER steering damper.:D
Thanks for the responses. It's a '97 220 in great shape. Bearings are tight, tires are straight. Perhaps it's just my inexperience. And like I say, I only noticed it at high speed on road surface. It' s like a rapid side-to-side vibration. Definitely not bad enough to wipe me out.