I realize it's been a long time since you wrote in, but there really isn't enough info here to be helpful to you. You don't say what type(s) of palms, where you live, if your palms are planted indoors or outdoors or what else you see going on. Maybe you mean spider mites? Spiders are known to be good predators in the garden, so if you have an abundance of spiders they are getting rid of other bugs.
If you have spider mites, that's not good.