Alisdair, thanks for the reply! I've watered these plants when they become dry, and they are in a typical succulent potting soil in an draining pot– though I did have two of them of them in a non-draining pot with other succulents last fall and that is about the time it started. I've read that these types of Aeoniums don't love being bone dry like others, and they are growing well, so I never figured it was my watering habit.
If they did contract a fungal infection, is there a way to treat it?