I think you have an infestation of mealybugs. http://bit.ly/13DL79w I've had them on houseplants and seen them on various field crops, though never on plum. But there are many species of these sucking insects, and they can be pesky to control.
The females of some species secrete the telltale cottony layers to protect themselves while they suck the juices from plant tissues, and as a protective tent under which to lay their eggs and protect their young.
All species of mealybugs secrete honeydew, which can cause a fungal infection called sooty mold that looks just like it sounds. You may see ants scurrying around on the infested leaves. I think I see a black ant in the photo on the far left. Adult ants eat honeydew. http://bit.ly/14wIbyj
They actually farm aphids and related insects such as mealybugs http://www.youtube.com/watch?v=wE1X_Q..., protecting the smaller insects from natural predators so they can continue "milking" their farm animals for sustenance. Amazing!
Insecticidal soap is the usual means of control for the soft-bodied aphids and mealybugs, but may cause toxic reactions in plums. http://bit.ly/13KHKtR Test a few leaves first to see how it affects them; if you see leaf damage, try diluting the solution.