Answer: Peonies are subject to a number of diseases and a wet spring encourages such problems. The symptoms sound like a fungal disease. Fungi can overwinter in the soil and attack plant parts as they emerge. You can provide some measure of control by removing and destroying affected plant parts.
The best method of limiting disease from year to year is to cut off, remove, and destroy all peony foliage every fall after frost. You may also wish to prune off and destroy all the blackened plant parts now; dip your pruners in rubbing alcohol between cuts to avoid spreading any disease to uninfected parts.
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