· Stephen Whatley's Answer
· Hi Karen.
It's sounds like what you have is a fungal condition known as powdery mildew.
I'm not fully aware of the weather conditions you are expirencing in your zone but it has a lot to to do with determining if this is the problem. Typically,humid conditions, along with shade,which I assume your peony's are planted in, can be a prime breeding ground for powdery mildew.
This fungus will not necessarily kill the plant,but weaken them,making them more suseptable to insects and diseases. If you find that this may be what's going on,I would like to recommend a solution for eradication.
Any type of horticultural oil, Neem oil in particular, is a good,well rounded product that should be available from from your indepandent garden center,that will not only take care of fungus,but also take care of insects and mites at the same time.
If at all possible you can upload a picture,I can try to give a more definitive answer as to what might be going on.
I hope this information gets you started and please feel free to ask any more questions regarding this,or any other matter you may have about yor landscape.