Thank you for the question.  Your daylilies look like they are suffering from leaf streak, a very common fungal disease aggravated by wet weather. This infection may kill some leaves but doesn't harm the roots.  It is best managed by dividing daylily clumps to avoid overcrowding, avoiding overhead watering when possible, removing infected leaves, and cleaning up all vegetation at the end of the season to avoid overwintering of the fungus. There are no fungicides labeled for control of this disease in daylilies and no cultivars known to be resistant.  Read here to learn more:  
http://www.extension.umn.edu/garden/yard-garden/flowers/diseases-of-daylilies/

Thank you for contacting Extension.

Anita,
Thanks much. I will follow your suggestions. Good to know that it won't harm the roots.