It sounds like you have powdery mildew. Powdery mildew is a common fungal disease that can affect many plants, especially in late summer. Usually the fungus is plant-specific, so the powdery mildew attacking your peony is different from what may be attacking lilacs.

In late summer, do not do anything to your peony. The flowers finished earlier in the season and everything will be dying down soon enough. Be sure to remove all infected plant material and throw it away.

In additions, a grey mold caused by botrytis peony blight can attack peonies. See helpful information here.

Learn more about growing peonies in our Guide to Herbacious Peonies.

For tips on a variety of gardening topics, see our Plant Information Guides.
- Courtesy of NYBG Plant Information Service