Red spider mites, perhaps? I would spray with a soap solution. Be careful to read the label on the "soap" you use to make your solution. Be sure you don't accidentally use a detergent.
I think about a teaspoonful of pure soap in a quart of water would be about right. You'll need to repeat the spraying every 7 to 10 days, to kill any new mites that hatch out. About 4 treatments should do the trick.
One caveat, though: Mites suck the juices out of plants. They don't have chewing mouthparts. So, if something is actually chewing/eating your plants, then you probably have some other critter, in addition to the mites.
"Isn't it enough to see that a garden is beautiful without having to believe that there are fairies at the bottom of it too?" - Douglas Adams