There is no built-in support for priorities. You can define priorities yourself using the userData property of each Notification. For example, you could establish a convention in your application whereby Notification.getUserData() returns an Integer that is the priority of the notification, and arrange for every Notification you emit to follow this convention.
In JMX 2.0, which will be part of JDK 7, we are planning to add an Event Service for better handling of Notifications; see <http://bugs.sun.com/bugdatabase/view_bug.do?bug_id=5108776>. We will probably also add a Priority property to javax.management.Notification. The Event Service will be able to deliver notifications in order of their Priority, by default, and will also allow you to specify a Comparator<Notification> to use a different order.
蒩monn McManus -- JMX Spec Lead -- http://weblogs.java.net/blog/emcmanus